sanjay˜kumar˜shukla fundamentals of fibre- reinforced soil

Developments in Geotechnical Engineering

Sanjay Kumar Shukla

Fundamentals of Fibre-Reinforced Soil Engineering

Developments in Geotechnical Engineering

Series editorsBraja M. Das, Henderson, USA

Nagaratnam Sivakugan, Townsville, Australia

More information about this series at http://www.springer.com/series/13410

Sanjay Kumar Shukla

Fundamentals ofFibre-Reinforced SoilEngineering

Sanjay Kumar ShuklaDiscipline of Civil and Environmental EngineeringSchool of Engineering, Edith Cowan UniversityPerth, WA, Australia

ISSN 2364-5156 ISSN 2364-5164 (electronic)Developments in Geotechnical EngineeringISBN 978-981-10-3061-1 ISBN 978-981-10-3063-5 (eBook)DOI 10.1007/978-981-10-3063-5

Library of Congress Control Number: 2017930411

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Preface

In the current construction practice, reinforcing the soil is an effective and reliable

ground improvement technique for increasing the strength and stability of the soil in

various applications, including retaining structures, embankments, foundations,

slopes and pavements. The concept of reinforcing the soil with natural materials

was originated in ancient times; however, the galvanized steel strips, having a high

tensile modulus, are the earliest modern form of soil reinforcement developed in

1966 in France. Later, the use of polymeric products, called the geosynthetics,started as the soil reinforcement along with several other applications of specific

geosynthetics to achieve different functions as separation, filtration, drainage, fluid

barrier and protection. In the noncritical structures, natural products, called the

geonaturals, are also used as the soil reinforcement. Unlike the metal strips, in

general, the geosynthetic and geonatural reinforcements have a much lower tensile

modulus. Geosynthetic reinforcements (woven geotextiles, geogrids, some

geocomposites, etc.) as well as geonatural reinforcements (bamboo, geocoir,

geojute, etc.) are generally used in the form of flexible sheets/mats/meshes. The

subject of geosynthetics and geonaturals and their applications are called the

geosynthetic engineering, and there are some textbooks and reference books avail-

able on this subject.

Reinforcing the soil with flexible, discrete fibres is not a new technique in

civil/geotechnical engineering. However, as the fibre inclusions bring several

technical, economic and environmental benefits, in recent years, a great deal of

interest has been created worldwide on the potential applications of fibres within the

soils and other similar materials, such as coal ashes and mine tailings. Fibres are

generally available in large amounts in natural and waste forms. In many countries,

waste fibres (plastic waste fibres, old tyre fibres, etc.) have been creating disposal

and environmental problems. Utilization of these fibres in constructions can solve

the disposal problems in a cost-effective and environmentally friendly manner.

Over the past 30–35 years, the laboratory and field research studies have shown

that the use of natural, synthetic and waste fibres as a tension-resisting element

and/or an admixture causes significant modification and improvement in the

v

engineering properties (strength, stiffness, permeability, compressibility, etc.) of

soils and other similar materials. The soil reinforced randomly with short, discrete

fibres is basically a composite material and is called the randomly distributed fibre-reinforced soil, or simply the fibre-reinforced soil. The studies indicate that a fibre-reinforced soil exhibits greater extensibility and a smaller loss of post-peak

strength; that is, compared to soil alone, the fibre-reinforced soil is more ductile.

Soils, especially cohesionless soils, can also be reinforced by the continuous fibres/

yarns. In this reinforcing system, a single monofilament is spun or injected in a

random pattern simultaneously with the deposition of soil in a specific application.

This book presents the fundamentals of the fibre-reinforced soils within five

chapters as an engineering subject, called the fibre-reinforced soil engineering. Nocomplete book is currently available on this subject. The book is primarily designed

and developed as a textbook as well as a student-centred learning resource for a

one-semester course for senior undergraduate and postgraduate students as a part of

a geotechnical/civil engineering programme. This course may be offered to stu-

dents as an elective in the universities/institutes/colleges. The material in all the

chapters of this book is presented clearly in simple and plain English and includes

the optimum amount of text, illustrations, tables, examples and questions for

practice. Each chapter includes many useful references, quoted in text and listed

at the end of the chapter, for further study. As the practical solution to an engineer-

ing problem often requires the application of engineering judgement and experi-

ence, which can be acquired by regular professional practice and self-study, an

attempt has been made to provide the practical experience, including the field

application guidelines and some case studies. The chapter summary presented at

the end of each chapter may help the readers in getting some key learning points

easily. Through this textbook, the readers can learn the subject without any major

assistance, and some readers can learn the subject even by self-reading only. Apart

from students, researchers and teachers, this textbook will be a valuable learning

resource for the practising engineers dealing with utilization of fibres in construc-

tions and infrastructure developments worldwide.

For a better learning of the concept of fibre-reinforced soils, it is important to

have an understanding of the basic soil properties and core principles of soil

mechanics, as presented in Chap. 1, along with the basic description of soil

reinforcement. Chapter 2 provides the basic details of fibre-reinforced soils, focus-

ing on fibres and their types, and phase concept along with a brief introduction to

the soil reinforced with continuous fibres and multioriented inclusions. Chapter 3

deals with the engineering behaviour of fibre-reinforced soils as reported by various

researchers based on their experimental investigations and analyses of test results.

Chapter 4 focuses on presenting the reinforcing mechanisms, the models of fibre-

reinforced soils and findings of some numerical studies. Chapter 5 covers the details

of field applications of fibre-reinforced soils, emphasizing on analysis and design

concepts, and field application experience and guidelines. The key research devel-

opments have been included as required throughout the book.

I would like to thank Swati Meherishi, senior publishing editor, Aparajita Singh,

RaagaiPriya ChandraSekaran, Rajeswari Sathiamoorthy and other staff at Springer

vi Preface

http://dx.doi.org/10.1007/978-981-10-3063-5_1

http://dx.doi.org/10.1007/978-981-10-3063-5_2

http://dx.doi.org/10.1007/978-981-10-3063-5_3

http://dx.doi.org/10.1007/978-981-10-3063-5_4

http://dx.doi.org/10.1007/978-981-10-3063-5_5

for their full support and cooperation at various stages of the preparation and

production of this textbook.

I wish to extend sincere appreciation to my wife, Sharmila, for her encourage-

ment and support throughout the preparation of the manuscript. I would also like to

thank my daughter, Sakshi, and my son, Sarthak, for their patience during my work

on this textbook at home.

Finally, I welcome suggestions from the readers and the users of this textbook

for improving its content in future editions.

Perth, 2017 Sanjay Kumar Shukla

Preface vii

Contents

1 Basic Description of Soil and Soil Reinforcement . . . . . . . . . . . . . . . 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Soil and Its Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Soil Properties and Core Principles of Soil

Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.4 Soil Reinforcement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.5 Fibre-Reinforced Soil Engineering . . . . . . . . . . . . . . . . . . . . . . . 17

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2 Basic Description of Fibre-Reinforced Soil . . . . . . . . . . . . . . . . . . . . 23

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.2 Fibres . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.3 Phases in a Fibre-Reinforced Soil Mass . . . . . . . . . . . . . . . . . . . . 32

2.4 Soil Reinforced with Continuous Fibres and Multioriented

Inclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

3 Engineering Behaviour of Fibre-Reinforced Soil . . . . . . . . . . . . . . . 45

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Factors Affecting the Engineering Behaviour . . . . . . . . . . . . . . . . 46

3.3 Shear Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

3.3.1 Observations in Direct Shear Tests . . . . . . . . . . . . . . . . . . 47

3.3.2 Observations in Triaxial Tests . . . . . . . . . . . . . . . . . . . . . 54

3.4 Unconfined Compressive Strength . . . . . . . . . . . . . . . . . . . . . . . . 65

3.5 Compaction Behaviour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77

3.6 Permeability and Compressibility . . . . . . . . . . . . . . . . . . . . . . . . 80

3.7 California Bearing Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.8 Load-Carrying Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92

3.9 Other Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

ix

4 Soil Reinforcing Mechanisms and Models . . . . . . . . . . . . . . . . . . . . 111

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

4.2 Basic Soil Reinforcing Mechanisms . . . . . . . . . . . . . . . . . . . . . . 111

4.3 Basic Models of Fibre-Reinforced Soils . . . . . . . . . . . . . . . . . . . . 116

4.3.1 Waldron Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.3.2 Gray and Ohashi (GO) Model . . . . . . . . . . . . . . . . . . . . . 117

4.3.3 Maher and Gray (MG) Model . . . . . . . . . . . . . . . . . . . . . 120

4.3.4 Ranjan, Vasan and Charan (RVC) Model . . . . . . . . . . . . . 121

4.3.5 Zornberg Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

4.3.6 Shukla, Sivakugan and Singh (SSS) Model . . . . . . . . . . . . 126

4.4 Other Models and Numerical Studies . . . . . . . . . . . . . . . . . . . . . . 134

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

5 Applications of Fibre-Reinforced Soil . . . . . . . . . . . . . . . . . . . . . . . . 145

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.2 Field Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145

5.3 Analysis and Design Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.4 Field Application Experience and Guidelines . . . . . . . . . . . . . . . . 161

5.5 Scope of Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181

x Contents

About the Author

Dr Sanjay Kumar Shukla is the founding editor-in-

chief of International Journal of Geosynthetics andGround Engineering (Springer International Publish-

ing). He is an associate professor and programme

leader of civil and environmental engineering at the

School of Engineering, Edith Cowan University,

Perth, Australia. He is also an adjunct professor at

the School of Civil and Chemical Engineering, VIT

University, Vellore, India, and a Distinguished Profes-

sor of Civil Engineering at the Institute of Engineer-

ing and Technology, Chitkara University, Himachal

Pradesh, India. He graduated in 1988 with a first-class

degree with distinction in civil engineering from BIT

Sindri (Ranchi University, Ranchi), India, and earned his MTech in civil engineer-

ing (engineering geology) in 1992 and PhD in civil engineering (geotechnical

engineering) in 1995 from the Indian Institute of Technology Kanpur, India. He

has over 20 years of teaching, research and consultancy experience in the field of

Civil (Geotechnical) Engineering. He is the author of ICE textbooks titled CorePrinciples of Soil Mechanics and Core Concepts of Geotechnical Engineering, andhas authored/co-authored/edited other 7 books and 12 book chapters. He is also the

author/co-author of more than 160 research papers and technical articles, including

over 100 refereed journal publications. He is a fellow of Engineers Australia,

Institution of Engineers (India) and Indian Geotechnical Society and a member of

the American Society of Civil Engineers (ASCE), International Geosynthetics

Society and Indian Roads Congress. He serves on the editorial boards of the

International Journal of Geotechnical Engineering, Ground Improvement, Geo-technical Research, Indian Geotechnical Journal, Cogent Engineering and

Advances in Civil Engineering, and he is the scientific editor of the Journal ofMountain Science.

xi

Chapter 1

Basic Description of Soil and SoilReinforcement

1.1 Introduction

For a better learning of the fundamentals of fibre-reinforced soil engineering

through this book, as presented in later chapters, basic characteristics of soil, core

principles of soil mechanics and an introduction to the soil reinforcement are

presented briefly in this chapter. For more details about the soil and its mechanics,

the readers can refer to the textbook titled Core Principles of Soil Mechanics byShukla (2014). This chapter also provides the list of commonly used tests, which are

generally conducted for investigating the engineering behaviour of fibre-reinforced

soils and developing the models to predict their behaviour. At the end, the subject of

fibres and their applications, called the ‘fibre-reinforced soil engineering’, is

defined with its importance.

1.2 Soil and Its Phases

Soil comprises all the materials in the surface layer of the Earth’s crust that areloose enough to be moved by a spade or shovel. According to Karl Terzaghi, soil is

a natural aggregate of mineral particles that can be separated by such gentle means

as agitation in water (Terzaghi et al. 1996).

Soil is a particulate and multiphase system consisting of, in general, three

phases, namely, solid, liquid and gas (Fig. 1.1). The space in a soil mass occupied

by liquid and/or gas is known as the void. A dry soil has air only in the void, while

the void volume of a fully saturated soil is occupied by water only. There are

several phase relationships and interrelationships; the most common ones are given

below, where V andW refer to volume and weight, respectively, and subscripts a, w,

s and v denote air, water, solid and void, respectively:

© Springer Nature Singapore Pte Ltd. 2017

S.K. Shukla, Fundamentals of Fibre-Reinforced Soil Engineering,Developments in Geotechnical Engineering, DOI 10.1007/978-981-10-3063-5_1

1

n ¼ Vv

Vð1:1Þ

e ¼ Vv

Vs

ð1:2Þ

S ¼ Vw

Vv

ð1:3Þ

w ¼ Ww

Ws

ð1:4Þ

γ ¼ W

Vð1:5Þ

γd ¼Ws

Vð1:6Þ

γs ¼Ws

Vs

ð1:7Þ

γsat ¼Wsat

Vð1:8Þ

γ0 ¼ γsat � γw ð1:9ÞG ¼ γs

γwð1:10Þ

Air/gas

Solid Air/gas

Water/liquid

(a) (b)

V

vVwV

aV

sV

0a ≈W

W

wW

sW

Water/liquid

Solid

Fig. 1.1 An element of soil mass: (a) phases in the natural state, (b) phases separated for

mathematical analysis

2 1 Basic Description of Soil and Soil Reinforcement

n ¼ e

1þ eð1:11Þ

Se ¼ wG ð1:12Þ

γ ¼ Gþ Se

1þ e

� �γw ¼ 1þ w

1þ e

� �Gγw ð1:13Þ

γd ¼Gγw1þ e

¼ Gγw1þ wG

S

¼ γ

1þ wð1:14Þ

where n is the porosity of soil, e is the void ratio of soil, S is the degree of saturationof soil, w is the water content of soil, γ is the total/bulk/wet/moist unit weight

(or simply unit weight) of soil, γd is the dry unit weight of soil, γs is the unit weightof soil solids, γsat is the saturated unit weight of soil, γw is the unit weight of water

(¼9.81 kN/m3), γ0 is the submerged/buoyant unit weight of soil, G is the specific

gravity of soil solids (i.e. soil particles or mineral matter) and Wsat is the saturated

weight of soil. The values of n, S and w are normally expressed as a percentage,

while the value of e is expressed as a decimal.

Note that massM and weightW, having SI units as kilogramme (kg) and newton

(N), respectively, of a soil element are related as

W ¼ Mg ð1:15Þ

where g is the acceleration due to gravity, which is taken as 9.81 m/s2 or sometimes

approximately as 10 m/s2 for simplicity. In most geotechnical engineering appli-

cations at various locations of the Earth, weight is preferred.

The total density (or simply density) ρ of a soil element is defined as

ρ ¼ M

Vð1:16Þ

where V is the volume of the soil element.

The unit weight γ and density ρ of a soil element are related as

γ ¼ ρg ð1:17Þ

For each of the unit weights (dry unit weight γd, unit weight of solids γs,saturated unit weight γsat, submerged unit weight γ0), you may define a

corresponding density (dry density ρd, density of solids ρs, saturated density ρs orsubmerged density ρ0) of the soil element as the total density is defined in

Eq. (1.16). You may also write relationships for other unit weights and densities

as done in Eq. (1.17), for example, γd¼ ρdg.

Example 1.1A cubical soil sample of 200-mm edge length is collected from the base level of a

proposed shallow foundation. Its mass is found to be 16.1 kg. Determine the total

unit weight of the soil.

1.2 Soil and Its Phases 3

SolutionFrom Eq. (1.15), the weight of soil sample,

W ¼ Mg ¼ 16:1ð Þ 9:81ð Þ ¼ 157:9 N

Since the soil sample is cubical, its volume,

V ¼ 0:2ð Þ3 ¼ 0:008 m3

From Eq. (1.5), the total unit weight,

γ ¼ 157:9

0:008¼ 19737:5 N=m3 � 19:74 kN=m3

Example 1.2An in situ soil has a total unit weight of 18.75 kN/m3 and a water content of 28%.

Determine the following:

(a) Void ratio

(b) Degree of saturation

Assume that the specific gravity of soil solids is 2.68.

Solution

(a) From Eq. (1.13), the total unit weight,

γ ¼ 1þ w

1þ e

� �Gγw

or, the void ratio,

e ¼ 1þ wð Þ Gγwγ

� �� 1 ¼ 1þ 0:28ð Þ 2:68� 9:81

18:75

� �� 1 ¼ 0:79

(b) From Eq. (1.12), the degree of saturation,

S ¼ wG

e¼ 0:28ð Þ 2:68ð Þ

0:79¼ 0:95 or 95%


1.3 Soil Properties and Core Principles of Soil Mechanics

Properties of soils are highly variable from one site to another, and even at a single

site, they can vary with locations. The air content of a soil has little engineering

significance, while the water content influences the engineering properties of soil

significantly. The design and stability of geotechnical structures are significantly

governed by the properties of soil, mainly permeability, compressibility and shear

strength. The subject dealing with the physical properties of soil and the behaviour

of soil masses in connection with their practical applications is known as the soil

mechanics. Most properties of soils are listed below:

1. Index/basic properties: total unit weight (γ), void ratio (e), specific gravity of

soil solids (G), water content (w), degree of saturation (S), particle-size distri-

bution, consistency limits [liquid limit (wL), plastic limit (wP), shrinkage limit

(wS)] for cohesive soils and relative density (Dr) for cohesionless soils

2. Compaction characteristics: maximum dry unit weight (γdmax) and optimum

water content (wopt)

3. Permeability: coefficient of permeability or hydraulic conductivity (k)4. Compressibility: compression index (Cc), recompression index (Cr), swelling

index (Cs), coefficient of volume change (mv), coefficient of consolidation (cv)and secondary compression index (Cα)

5. Shear strength: total stress-strength parameters as cohesion intercept (c) andangle of shearing resistance (ϕ) and effective stress-strength parameters as

effective cohesion intercept (c0) and effective angle of shearing resistance (ϕ0)6. Stiffness: elastic constants, such as Young’s modulus of elasticity (E), shear

modulus of elasticity (G), bulk modulus of elasticity (K ) and Poisson’s ratio (μ)

The core concepts of soil mechanics are briefly described below (Shukla 2014):

• The term ground refers to soil, rock and/or fill in place prior to the execution of

the construction projects. Based on the method of formation, soils are classified

as residual soils, sedimentary soils, organic soils and fills (or man-made soils).

• The smallest particle size which can be seen with naked eye is typically

0.075 mm. Clay (< 0.002 mm), silt (0.002–0.075 mm), sand

(0.075–4.75 mm), gravel (4.75–80 mm), cobble (80–300 mm) and boulder

(>300 mm) are the names of particle sizes, and they are also often used to

describe soils. The dividing lines between the size limits are arbitrary and vary

with different classification systems. Silt-size and clay-size particles are collec-

tively called the fines. A fine-grained soil has fines 50% or more (by dry weight)

of soil, while the coarse-grained soil has fines less than 50% (by dry weight)

of soil.

• The classification of a soil requires the particle-size distribution based on sieve

analysis and consistency limits (liquid and plastic limits). If a soil is described as

a silty clay, then the clay content is greater than the silt content in the soil.

• The soil is called a well-graded soil if the distribution of the particle sizes

extends over a large range. The soil consisting of particles of almost one size

1.3 Soil Properties and Core Principles of Soil Mechanics 5

is called the uniformly graded soil. If a soil has an excess of certain particle sizes

and a deficiency of other sizes, then the soil is called the poorly graded soil.• Soil particles and water are almost incompressible, so any volume change in a

saturated soil is equal to the volume of water that drains out of or into the soil.

• For a dry soil, the degree of saturation, S¼ 0%, and for a fully saturated soil,

S¼ 100%. For a partially saturated soil, S lies between 0 and 100%. The natural

water content w of soils can exceed 100% although it is well under 100% for

most soils.

• Typical values of saturated unit weight of some common soils are as follows:

19–24 kN/m3 for sands and gravels, 14–21 kN/m3 for silts and clays and

10–11 kN/m3 for peats.

• In the absence of measured values, it is a common practice to assume G¼ 2.65

for sand and G¼ 2.70 for clay.

• The difference, wL�wP, is called the plasticity index (IP), which is used in

strength correlations and for estimating some compressibility parameters.

• If the natural water content (w) of a soil is close to its liquid limit (wL), the soil is

normally consolidated, while for a medium to heavily overconsolidated soil, w is

close to its plastic limit wP (Bowles 1996).

• The consistency of a cohesionless/granular soil is generally described in terms of

relative density defined as

Dr ¼ emax � e

emax � emin

� �� 100% ð1:18Þ

or

Dr ¼ γd � γd min

γd max � γd min

� �γd max

γd

� �� 100% ð1:19Þ

where e is the in situ (or in-place) void ratio of soil; emin is the minimum void ratio,

i.e. void ratio in the densest possible state of soil; emax is the maximum void ratio,

i.e. void ratio in the loosest possible state of soil; γd is the in situ (or in-place) dry

unit weight of soil; γd min is the minimum dry unit weight, i.e. dry unit weight in the

loosest possible state of soil; and γd max is the maximum dry unit weight, i.e. dry

unit weight in the densest possible state of soil.

• The consistency of the coarse-grained soil is described as very loose (0% <Dr< 15%), loose (15% <Dr< 35%), medium (35% <Dr< 65%), dense

(65% <Dr< 85%) and very dense (85% <Dr< 100%).

• The total vertical stress at a depth z from the ground surface can be computed as

σv ¼ γ z ð1:20Þ

where γ is the total unit weight of the soil.


• Within a saturated soil mass, the effective vertical stress σ0v at any depth is equalto the total vertical stress σv minus the pore water pressure u at that depth. Thus,

σ0v ¼ σv � u ð1:21Þ

Equation (1.21) states Terzaghi’s effective stress principle.

• For water table below the ground surface, a rise in the water table causes a

reduction in the effective stress at any point within the soil. For water table

above the ground surface, a fluctuation in the water table does not alter the

effective stress at any point within the soil.

• The permeability of a soil indicates its ability to conduct fluid, and it depends on

the characteristics of both the soil and the permeant. The flow through a soil

mass may be estimated using Darcy’s law, which is stated as

v ¼ ki ð1:22Þ

where v is the flow or discharge velocity of water through an element of the soil

mass, i¼Δh/L is the hydraulic gradient causing the flow, Δh being the hydraulic

head causing the flow, L is the length of soil element in the direction of the flow, and

k is the coefficient of permeability or hydraulic conductivity of soil. Equation (1.22)

holds good for most soils, especially finer than coarse sands, in which the flow can

be laminar. The permeability of sands ranges from 10�2 to 10�5 m/s while that of

clays is equal to or less than 10�9 m/s.

• As water can only flow through the voids in the cross section of the soil mass, the

average effective velocity of flow, called the seepage velocity vs, is greater thanthe discharge velocity v. The value of vs can be determined by using the

following relationship:

vs ¼ v

n¼ ki

nð1:23Þ

where n is the porosity of soil.

• Above the water table, the pore water pressure is negative due to surface tension,

and so there is suction, which can be as high as 6 kPa in fine sand and 600 kPa

in clay.

• When water flows through a soil, it exerts force, called the seepage force, on the

soil particles through friction drag. In an isotropic soil, the seepage force always

acts in the direction of flow. If h is the loss in total head through friction drag

over length L of the soil and A is the area of cross-section through which water

flows, then the seepage force is

J ¼ γwhA ¼ iγw ALð Þ ¼ iγwV ð1:24Þ

where γw is the unit weight of water and V is the total volume of the soil mass.


• The seepage force per unit volume of soil, called the seepage pressure, is

j ¼ J

V¼ iγw ð1:25Þ

• As an upward flow of water through a soil mass causes a decrease in effective

stress, there is a possibility of zero effective stress within the soil mass at a

certain hydraulic gradient, known as the critical hydraulic gradient ic , which canbe calculated as

ic ¼ G� 1

1þ eð1:26Þ

where G is the specific gravity of soil solids and e is the void ratio of soil.

• Under the influence of seepage, which can take place in the downstream of Earth

dams and other water-retaining structures in the upward direction, the founda-

tion soil particles can continuously move in the seepage direction, if the hydrau-

lic gradient exceeds the critical hydraulic gradient. This phenomenon of soil

movement is known as the soil piping. Piping resistance of soil acts in the

direction opposite to seepage force and is equal to the seepage force at which soil

particles start moving due to the seepage of water.

• The factor of safety against piping, FSpiping, is defined as

FSpiping ¼ icie

ð1:27Þ

where ie is the maximum exit hydraulic gradient, that is, the maximum hydraulic

gradient near the discharge boundary surface. For no piping, FSpiping> 1.

• Compaction refers to the volume reduction of an unsaturated soil mass due to

expulsion of air from its voids/pores caused by the external compressive load/

stress application. Compaction differs from the consolidation, which is a time-

dependent process of volume reduction of mainly a saturated soil mass due to

expulsion of water from its voids/pores.

• Within a soil mass, the ratio of effective horizontal stress (σ0h) to effective verticalstress (σ0v), called the lateral stress ratio (K), is typically in the range of 0.2–0.5.

• The compressibility of a soil is a function of soil type/composition, effective

stress and stress history. The compression index Cc is used to determine the

magnitude of primary consolidation settlement of a normally consolidated soil.

The coefficient of consolidation cv is used to determine the rate of settlement

during the primary consolidation.

• The ratio of maximum past effective vertical stress σ0vmax to the present effective

vertical stress (σ0v0) is called the overconsolidation ratio (OCR), which is used toexpress the degree of overconsolidation (or stress history) of soil. Thus,


OCR ¼ σ0vmax

σ0v 0ð1:28Þ

For normally consolidated soils, OCR¼ 1, and for overconsolidated soils,

OCR> 1.

• The maximum internal resistance per unit area of a soil to applied shear stress is

called its shear strength. A soil is rarely required to resist tension, and generally

fails in shear even though the applied load is compressive. Therefore, the

analysis of strength of a soil is basically a problem of shear strength. The

shear strength τf appears as the shear stress on the failure plane within the soil

mass at failure, and its SI unit is N/m2 or pascal (Pa). It is commonly expressed

as the Mohr-Coulomb failure criterion, which is stated as

τf ¼ c0 þ σ0f tanϕ0 ð1:29Þ

where σ0f is the effective normal stress on the failure plane at failure, c0is called

the effective cohesion (also known as the effective cohesion intercept) and ϕ0is

called the effective angle of internal friction (also known as the effective angle

of shearing resistance, or simply effective friction angle).

• Since a coarse-grained soil has almost no cohesion, its shear strength depends

mainly on the internal friction between the particles. Such soils are called

cohesionless, granular, frictional or free-draining soils. A fine-grained soil

consists of a significant amount of silt-size and clay-size particles, and therefore

its shear strength depends on cohesion as well as internal friction between the

particles. Such soils are called cohesive or cohesive-frictional soils depending on

the relative significance of cohesion and internal friction between the particles.

• The triaxial compression test is the most versatile test for studying strength and

stiffness (stress-strain relationship) properties of a soil. A triaxial test has the

following three types: consolidated-drained (CD), consolidated-undrained

(CU) and unconsolidated-undrained (UU) tests, depending on the loading con-

ditions simulated as per the field requirements. The stress-strain behaviour of

loose sand is similar to that of normally consolidated clay, whereas dense sand

behaves similar to overconsolidated clay. A clay subjected to undrained/quick

loading or unloading with a constant volume behaves as a purely cohesive

material which has angle of shearing resistance equal to zero, and therefore

the shear strength, called the undrained shear strength, is

τf ¼ cu ¼ qu2

ð1:30Þ

where cu is the undrained cohesion and qu is the unconfined compressive

strength of soil.


• The shear strength of a cohesive soil increases with time from τf¼ cu under

undrained loading to τf ¼ c0 þ σ0f tanϕ0 under drained loading as the pore water

escapes from the voids, resulting in a decrease in pore water pressure. There is a

possibility of a decrease in shear strength of soil as a result of unloading by

excavation, an increase in pore water pressure caused by changes in groundwater

condition or in seepage pressure, or softening of fissures/cracks present in stiff

clays. Shear strength is generally computed for the most critical condition which

usually exists immediately upon load application or immediately after construc-

tion as an undrained loading (Teng 1962).

• A granular soil is generally an excellent foundation material and the best

embankment and backfill material, while a clayey soil is a very poor material

for foundation, embankment and backfill. Clay is nearly watertight because of its

low permeability, and therefore, it is the best soil material for construction of

impervious layers/liners/barriers for ponds and landfills.

• A cohesive soil generally loses a portion of its shear strength upon remoulding/

disturbance. If the unconfined compression test is conducted on both the

undisturbed and remoulded specimens of the same cohesive soil at an unaltered

water content, the effect of remoulding/disturbance, that is, the amount of

strength loss, may be expressed in terms of sensitivity St, defined as

St ¼qu undisturbedð Þqu remouldedð Þ

¼ cu undisturbedð Þcu remouldedð Þ

ð1:31Þ

Based on the sensitivity, clays are classified as insensitive (St¼ 1), low sensitive

(St¼ 1� 2), medium sensitive (St¼ 2� 4), highly sensitive (St¼ 4� 8), extra sen-

sitive (St¼ 8� 16) or quick (St> 16).

• Swelling and shrinkage characteristics of highly plastic clays due to the presence

of mainly montmorillonite mineral cause damages to foundations, pavements

and other structures.

• An organic soil has a spongy structure, low shear strength, high compressibility,

acidity and injurious characteristics to construction materials, and therefore, it is

not a suitable foundation material. It undergoes creep (continued compressions

at constant effective stress), which contributes significantly to long-term

settlement.

• An unsaturated soil gains a part of its strength from the suction of capillary water

within the voids, but this strength is lost when the soil becomes saturated, thus

resulting in collapse of soil structure with a significant deformation/settlement.

• A retaining wall is usually constructed to support a soil, rock or any other soil-

like material (coal ash, mine tailing, etc.) that cannot remain stable with a

vertical or sloping face. The stability of a retaining wall or other similar structure

(abutment, basement wall, sheet pile wall, etc.) depends on the amount of lateral

earth pressure from the soil, called the backfill, supported by the wall.

• The stability of a soil slope is significantly governed by the shear strength of

the soil.


• The term ‘foundation’ refers to the load-carrying structural member of an

engineering system (e.g. building, bridges, road, runway, dam, tower, pipeline

or machine) constructed on or below the ground surface as well as the soil/rock

mass that finally supports the loads from the engineering system. The load per

unit area at the base level of the structural part of the foundation (often called the

footing) that causes the shear failure to occur in the soil is termed the ultimatebearing capacity or simply the bearing capacity of the foundation. The bearingcapacity of a foundation greatly depends on the shear strength of the foundation

soil in addition to other factors such as shape and size of the foundation, depth of

foundation, water table location and load inclination to the vertical.

Example 1.3A soil deposit has a void ratio of 0.85. If the void ratio is reduced to 0.60 by

compaction, determine the percentage volume reduction due to compaction.

SolutionWithin the soil deposit, consider a soil element with V as its total volume, Vv as the

void volume and Vs as the solid volume. Given, initial void ratio, e¼Vv/Vs¼ 0.85;

and void ratio after compaction, e1¼Vv1/Vs¼ 0.60, Vv1 being the void volume after

compaction.

If p is the percentage volume reduction due to compaction, then

p ¼ Vv � Vv1

V

� �� 100%

Considering the basic definitions of phase relationships and substituting the

values,

p ¼ Vv � Vv1

V

� �� 100% ¼ Vv � Vv1

Vv þ Vs

� �� 100%

¼ Vv=Vs � Vv1=Vs

Vv=Vs þ 1

� �� 100% ¼ e� e1

eþ 1

� �� 100%

or

p ¼ 0:85� 0:60

0:85þ 1

� �� 100% ¼ 13:5%

Example 1.4If the unconfined compressive strength of saturated clay is 40 kPa, what will be its

undrained shear strength? Can you describe the consistency of this soil?

SolutionGiven, unconfined compressive strength, qu¼ 40 kPa. From Eq. (1.30), the

undrained shear strength is


cu ¼ qu2¼ 40

2¼ 20 kPa

As 12.5 kPa< cu< 25 kPa, the soil is soft.Note: The following are the descriptive terms for consistency of cohesive soils:

Very soft (cu< 12.5 kPa), soft (12.5 kPa< cu< 25 kPa), firm (25

kPa< cu< 50 kPa), stiff (50 kPa< cu< 100 kPa), very stiff (100

kPa< cu< 200 kPa) and hard (cu> 200 kPa).

1.4 Soil Reinforcement

Soil supports the structural foundations, and it is used as a construction material in

various civil/geotechnical engineering projects. Soil and other similar materials,

such as fly ash, mine tailings, etc., are strong in compression but weak in tension. In

the current construction practice in civil and environmental engineering as well as

in some mining, agricultural and aquacultural engineering projects, various types

and forms of reinforcement materials are introduced to improve the engineering

properties (e.g. strength, stiffness, permeability, compressibility, etc.) of soil and

other similar materials, thereby resulting in relatively a new material, called the

reinforced soil. Thus a reinforced soil is a composite material in which tension-

resisting elements are embedded in a soil mass, which is weak in tension.

The concept of soil reinforcement is not new as soils have been reinforced since

prehistoric times. In nature, even some insects, birds and animals use soil rein-

forcement in suitable forms for creating different structures as they need to meet

their requirements. However, the modern form of soil reinforcement was first

developed by Vidal (1966, 1969) in the form of steel/metal strips, and the

reinforced soil was patented in the name of Reinforced Earth (Schlosser and

Long 1974). The metal strips are available with smooth or ribbed surfaces. To

avoid the corrosion problem, the steel strips are often galvanized suitably to

maintain their designed life within the soil mass.

In most applications, soil reinforcement is often used nowadays in the form of

continuous geosynthetic or geonatural reinforcement inclusions (e.g. sheets, nets,

meshes, grids, strips or bars) within the soil mass in a definite pattern, resulting in

the systematically reinforced soil. For more details on such systematically

reinforced soils, called the geosynthetic-reinforced soils (ply soils by McGown

and Andrawes 1977), which are studied under the subject of geosynthetic engineer-ing, the readers can refer to the books by Shukla (2002, 2006, 2012, 2016) and

Koerner (2012). Note that the geosynthetic or geonatural reinforcements as well as

the metal strips are normally oriented in a preferred direction; thus, the reinforce-

ment orientation is generally one dimensional and is installed sequentially in

alternating layers as per the design requirements of the specific application. Fig-

ure 1.2 illustrates an example of the systematically reinforced soil. The geotextile-

reinforced backfill helps reduce the lateral earth pressure significantly, thereby


decreasing the thickness of the wall. With the geosynthetic-reinforced soil backfill,

there is a possibility to completely avoid the construction of a thick wall by

providing a thin skin face to mainly prevent the surface soil erosion.

With respect to stiffness (modulus of elasticity), steel and fibreglass reinforce-

ments in the form of strips and bars having a high modulus of elasticity are often

categorized as ideally inextensible reinforcements, while the geosynthetic and

geonatural reinforcements, including plant roots, having relatively low modulus

of elasticity, are considered ideally extensible reinforcements. The distinction

between the two categories of soil reinforcement, ideally inextensible reinforce-

ments and ideally extensible reinforcements, was explained by McGown et al.

(1978) in terms of a ratio of reinforcement tensile (longitudinal) modulus of

elasticity (EReinforcement) to average soil modulus of elasticity (ESoil) as follows:

for ideally inextensible reinforcements,

EReinforcement

ESoil

> 3000 ð1:32Þ

and for ideally extensible reinforcements,

EReinforcement

ESoil

< 3000: ð1:33Þ

The difference between the influences of inextensible and extensible reinforce-

ments is significant in terms of the stress-strain behaviour of the reinforced soil

system, as noted in Fig. 1.3 (McGown et al. 1978). The soil reinforced with

extensible reinforcement, termed ply soil by McGown and Andrawes (1977), has

greater extensibility (ductility) and smaller loss of post-peak strength compared to

soil alone or soil reinforced with inextensible reinforcement, termed ReinforcedEarth by Vidal (1966, 1969). The inextensible reinforcements generally have

rupture strains smaller than the maximum tensile strains in the unreinforced soil,

thereby resulting in catastrophic failures, while the extensible reinforcements may

have rupture strains larger than the maximum tensile strains in the unreinforced

soil, thus they seldom rupture.

Retaining wall

Woven geotextile layers within the soil backfill

Fig. 1.2 A retaining wall

supporting a systematically

reinforced soil backfill

1.4 Soil Reinforcement 13

In spite of some differences in the behaviour of inextensible and extensible

reinforcements, a similarity between them exists in that both significantly

strengthen the soil and inhibit the development of internal and boundary deforma-

tions of the soil mass by developing tensile stresses in the reinforcement. Thus, both

forms of reinforcements are tensile strain inclusions.

12

8

4

00 2 4 6 8 10

Sand and strong inextensible inclusion

Sand and strong extensible inclusion

Inclusion

Sand alone

Sand and weak inextensible inclusion

Sand and weak extensible inclusion

Axial strain, (%)1ε

1σ

1σ

3σ3σ

2/1δ

2/1δ

2/3δ2/3δ

12

8

4

00 2 4 6 8 10

Sand and strong

a

b

inextensible inclusion

Sand and strong extensible inclusion

Sand alone

Sand and weak inextensible inclusion

Sand and weak extensible inclusion

Axial strain, (%)1ε

Str

ess

ratio

, s1

/ s3

Str

ess

ratio

, s1

/ s3

Fig. 1.3 Postulated behaviour of a unit cell in plane strain conditions with and without inclusions:

(a) dense sand with inclusions, (b) loose sand with inclusions (Adapted from McGown et al. 1978)


Note that it is not always necessary to reinforce the soil with a reinforcement

having a very high modulus as compared to the modulus of soil alone as some

structures may be allowed to strain significantly without any functional failure.

In the past few decades (30–35 years), experimental and mathematical studies

have been conducted to investigate the behaviour of soil reinforced randomly with

different types of discrete, flexible, synthetic and natural fibres, called the randomlydistributed/oriented fibre-reinforced soils (RDFRS), or simply the fibre-reinforcedsoils (FRS), with an intention of improving the soil strength and other engineering

characteristics (Shukla et al. 2009; Shukla 2016). Within the fibre-reinforced soil,

the fibre arrangement is basically two dimensional or three dimensional, depending

on their placement or mixing. In field applications, the one-dimensional arrange-

ment of fibres in any specific direction within the soil mass is a difficult task, and so

no effort is made to consider this one-dimensional arrangement. In general, the

reinforced soil is obtained by mixing the soil and fibres in such a way that the fibres

are introduced into the soil mass randomly and homogeneously. The quality of

mixing is very important to avoid any planes of weakness, such as those parallel to

the oriented reinforcement, or even very small portions with insufficient fibre

content. Figure 1.4 illustrates an example of the randomly distributed fibre-

reinforced soil. The fibre-reinforced backfill also helps reduce the lateral earth

pressure significantly, thereby decreasing the thickness of the wall, as the system-

atically reinforced soil backfill works.

The concept of reinforcing soil with fibres, especially the natural ones, origi-

nated in the ancient times in some applications. Civilizations in Mesopotamia

added straws to mud bricks to provide integrity to a weak matrix by arresting the

growth of cracks (Majundar 1975; Hoover et al. 1982). For example, the use of

natural fibres in composite construction can be seen even today in the rural areas of

some countries, such as India. In fact, the scientific interest in the fibre reinforce-

ment of soils began in the 1970s with an attempt to estimate the influence of plant

and tree roots on the stability of earth slopes (Waldron 1977). Subsequently, the

randomly distributed fibre-reinforced soils have attracted increasing attention in

geotechnical engineering for their field applications.

Retaining wall Fibres within

the soil backfill

Fig. 1.4 A retaining wall

supporting a randomly

distributed fibre-reinforced

soil backfill

1.4 Soil Reinforcement 15

Note that synthetic and natural fibres, including the plant roots, behave as

extensible reinforcements as they have relatively a lower modulus of elasticity.

Chapter 2 presents the basic description of fibre-reinforced soils, and their engi-

neering behaviour, as studied by the researchers worldwide, is described in Chap. 3.

You will notice that several laboratory tests and some field tests have been used to

investigate the behaviour of fibre-reinforced soils. Some of these tests are listed

below:

• Direct shear test

• Static and cyclic triaxial compression tests

• Unconfined compression test

• Compaction test

• Hydraulic conductivity test

• Consolidation test

• California bearing ratio (CBR) test• Plate load test

• Brazilian indirect/splitting tensile strength test

• Durability test

• Ring shear test

• Torsional shear test

• Bender element test

• Resonant column test

• Flexural strength test

• Fibre pullout test

All these tests, which have originally been developed for assessing the charac-

teristics of unreinforced/plain soils, are also conducted in accordance with relevant

standards (e.g. ASTM standards), as applicable in the specific study/project. Direct

shear, static triaxial compression and unconfined compression tests have been

widely used to investigate the strength behaviour of fibre-reinforced soils, consid-

ering variations in several parameters, including the fibre characteristics, as

discussed in Chap. 2. CBR and plate load tests are conducted to obtain the results

for direct applications in the design of pavement layers and shallow foundations.

Brazilian indirect/splitting tensile test is an indirect method of applying tension

through splitting. The stresses developed during a splitting tensile test are analysed

using the theory of elasticity. The original ring shear apparatus was developed by

Bishop et al. (1971). The effect of fibre reinforcement at very large strains (higher

than those possible in triaxial compression tests) is generally evaluated by ring

shear tests. Bender elements test, introduced by Shirley and Hampton (1978), is

commonly conducted for determining the elastic shear modulus of soil at very small

strains. Bender element system is often set up in the triaxial compression test, but it

can also be set up in other laboratory tests. The fibre-soil interface friction angle can

be determined by fibre pullout test in a modified shear box apparatus.

Based on the observations in the experimental studies, attempts have been made

by the researchers to present the models to predict their behaviour of fibre-

reinforced soil, as described in Chap. 4.


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In the current construction practice, discrete, flexible, synthetic and natural fibres

have several field applications, as described in Chap. 5, in conjunction with soils

and other similar materials, such as coal ashes, mine wastes, etc.

1.5 Fibre-Reinforced Soil Engineering

The subject of fibres and their applications in conjunction with soils and other

similar materials, such as coal ashes, mine wastes, etc., is known as the ‘fibre-reinforced soil engineering’, which can be defined as follows:

Fibre-reinforced soil engineering deals with the application of scientific principles and

methods to the acquisition, interpretation and use of knowledge of fibre products for the

solution to the problems in geotechnical, transportation, geoenvironmental and hydraulic

engineering.

As the fibres are used in conjunction with soils and other similar materials, they

are often called the geofibres. Throughout this book, the term fibres always refer to

the geofibres.

This book presents the fundamentals of fibre-reinforced soil engineering, focus-

ing on use of fibres in different areas of civil engineering as this subject has been

defined. The soil can also be reinforced randomly with continuous fibres or

multioriented (three dimensional, 3D) inclusions. Some details for these reinforced

soils are also provided in Chap. 2. Note that some wastes, such as the municipal

solid wastes, may be physically similar to randomly distributed fibre-reinforced

soils, and, therefore, the concepts of fibre-reinforced soil engineering, as presented

in this book, are equally applicable to such wastes to manage their disposal and

utilization in engineering practice. Also note that characteristics of fibre-reinforced

soils and their applications as described in this book may also be applicable to some

mining, agricultural and aquacultural projects, which are very similar to some civil

engineering projects.

Note that fibre reinforcement is not only alternative ground improvement tech-

nique, but it may also make several construction projects cost-effective as well as

environmentally friendly. As fibres can be obtained from many waste products,

such as old and used tyres, used plastic materials, etc., their utilization can greatly

help solve waste disposal problems; otherwise, a significant volume of the landfills

can be occupied by these wastes. Thus the fibre-reinforced soil engineering has

become a subject of special importance in civil engineering and other related fields.

Chapter Summary

1. Soil is a particulate and multiphase system consisting of, in general, three

phases, namely, solid, liquid and gas. There are several phase relationships

and interrelationships.

2. The classification of a soil requires the particle-size distribution based on sieve

analysis and consistency limits (liquid and plastic limits).

1.5 Fibre-Reinforced Soil Engineering 17

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3. Soil particles and water are almost incompressible, so any volume change in a

saturated soil is equal to the volume of water that drains out of or into the soil.

4. The design and stability of geotechnical structures are significantly governed

by the properties of soil, mainly permeability, compressibility and shear

strength.

5. A granular soil is generally an excellent foundation material and the best

embankment and backfill material, while a clayey soil is a very poor material

for foundation, embankment and backfill. Clay is nearly watertight because of

its low permeability, and therefore, it is the best soil material for construction of

impervious layers/liners/barriers for ponds and landfills.

6. The reinforced soil is a composite material that consists of soil mass (or other

similar material) and some form of reinforcement material (inextensible such

as steel strips or extensible such as geosynthetics or fibres), which provides an

improvement in the engineering characteristics (e.g. strength, stiffness, perme-

ability, compressibility, etc.) of soil.

7. The reinforcement can be included into a soil mass systematically or randomly,

resulting in systematically reinforced soil (e.g. geosynthetic-reinforced soil)

and randomly distributed fibre-reinforced soil, respectively.

8. The inextensible reinforcements generally have rupture strains smaller than the

maximum tensile strains in the unreinforced soil, thereby resulting in cata-

strophic failures, while the extensible reinforcements may have rupture strains

larger than the maximum tensile strains in the unreinforced soil, thus they

seldom rupture.

9. The behaviour of fibre-reinforced soils is generally studied by conducting the

tests developed for unreinforced soils with minor changes in some cases.

10. The subject of fibres and their applications in conjunction with soils and other

similar materials, such as coal ashes, mine wastes, etc., is known as the ‘fibre-reinforced soil engineering’, which provides cost-effective and environmen-

tally friendly solutions in a sustainable manner for several construction projects

in civil engineering and some other related areas.

Questions for Practice(Select the most appropriate answer to the multiple-choice questions from Q1.1 to

Q1.5.)

1.1. A soil has a water content of 320%. This statement

(a) Can be correct

(b) Is incorrect

(c) Has no physical meaning

(d) Often holds good at most construction sites

1.2. Within a silty sandy soil,

(a) Silt content is higher than sand content

(b) Sand content is higher than silt content


(c) Sand content is equal to silt content

(d) Clay content is always zero

1.3. Within a medium dense sandy soil mass, saturated by a rise of water table

above the ground surface, the effective stress at a depth of 5 m below the

ground surface can be approximately

(a) 0

(b) 25 kPa

(c) 50 kPa

(d) 100 kPa

1.4. Which of the following is an extensible reinforcement?

(a) Steel

(b) Woven geotextile

(c) Polyester fibre

(d) Both (b) and (c)

1.5. Which of the following soils when loaded fails at relatively large strain?

(a) Dense sand reinforced with strong inextensible reinforcement

(b) Dense sand reinforced with strong and extensible reinforcement

(c) Loose sand reinforced with strong inextensible reinforcement

(d) Dense sand with weak inextensible reinforcement

1.6. Differentiate between void ratio and porosity of a soil. How can you deter-

mine the void ratio of a soil?

1.7. What are the index properties of soils? What is their importance in field

applications?

1.8. What is relative density? Is it applicable to all types of soil? Can it be greater

than unity? Explain briefly.

1.9. What is the effect of surcharge loading on the effective stress?

1.10. How does consolidation differ from compaction?

1.11. Name three most important properties of soil.

1.12. Discuss the terms used to describe consistency of cohesive and cohesionless

soils.

1.13. What is the importance of critical hydraulic gradient? Give a field example of

its application.

1.14. How does a CD triaxial compression test differ from a UU triaxial compres-

sion test? Which one is a quick test?

1.15. For a partially saturated soil deposit at a project site, water content, w¼ 12%,

void ratio, e ¼ 0.55, and specific gravity of soil solids, G ¼ 2.66. Determine

the weight of water required to fully saturate 10 m3 of soil.

1.16. The plastic and liquid limits of a soil are 14 and 29, respectively. What is the

plasticity index of the soil? Can a soil have no plasticity index?

1.17. What is the theoretical maximum dry unit of a soil whose solid particles have

a specific gravity of 2.67?

1.5 Fibre-Reinforced Soil Engineering 19

1.18. Differentiate between a systematically reinforced soil and a randomly dis-

tributed fibre-reinforced soil. Explain with the help of some examples of

these reinforced soils.

1.19. What is basis for classifying the reinforcements as inextensible or extensible?

1.20. Do Reinforced Earth and ply soil refer to the same reinforced soil?

1.21. List the tests, which are used to study the behaviour of fibre-reinforced soils?

What problems do you expect while testing such soils by conventional tests,

which have been originally developed for soils without reinforcement?

1.22. How can concepts of fibre-reinforced soil engineering benefit the

community?

1.23. Visit a local construction site where fibres are being used. Observe the

challenges being faced during their introduction into soils.

Answers to Selected Questions

1.1 (a)

1.2 (b)

1.3 (c)

1.4 (d)

1.5 (b)

1.15 14.7 kN

1.16 15, Yes

1.17 26.19 kN/m3

References

Bishop AW, Green GE, Garga VK, Andersen A, Brown JD (1971) A new ring shear apparatus and

its application to the measurement of residual strength. Geotechnique 21(4):273–328

Bowles JE (1996) Foundation analysis and design, 5 edn. McGraw-Hill, New York

Hoover JM, Moeller DT, Pitt JM, Smith SG, Wainaina NW (1982) Performance of randomly

oriented fiber-reinforced roadway soils – a laboratory and field investigation. Iowa DOT

project report HR-211, Department of Civil Engineering, Engineering Research Institute,

Iowa State University, Ames

Koerner RM (2012) Designing with geosynthetics, vols 1 and 2, 6 edn. Xlibris, Bloomington

Majundar AJ (1975) Prospects of fiber reinforcements in civil engineering materials. Proceedings

of the conference at Shirley Institute of Fibers in Civil Engineering, Manchester, England

McGown A, Andrawes KZ (1977) The influence of nonwoven fabric inclusions on the stress-strain

behaviour of a soil mass. In: Proceedings of international conference on the use of fabrics in

geotechnics, Paris, pp 161–166

McGown A, Andrawes KZ, Al-Hasani MM (1978) Effect of inclusion properties on the behaviour

of sand. Geotechnique 28(3):327–346

Schlosser F, Long N-T (1974) Recent results in French research on reinforced earth. J Constr Div

ASCE 100(3):223–237

Shirley DJ, Hampton LD (1978) Shear-wave measurements in laboratory sediments. J Acoust Soc

Am 63(2):607–613


Shukla SK (2002) Geosynthetics and their applications. Thomas Telford, London

Shukla SK (2012) Handbook of geosynthetic engineering, 2 edn. ICE Publishing, London

Shukla SK (2014) Core principles of soil mechanics. ICE Publishing, London

Shukla SK (2016) An introduction to geosynthetic engineering. CRC Press/Taylor and Francis,

London

Shukla SK, Yin J-H (2006) Fundamentals of Geosynthetic Engineering. Taylor and Francis,

London

Shukla SK, Sivakugan N, Das BM (2009) Fundamental concepts of soil reinforcement – an

overview. Int J Geotechn Eng 3(3):329–343

Teng WC (1962) Foundation design. Prentice-Hall, Englewood Cliffs

Terzaghi K, Peck RB, Mesri G (1996) Soil mechanics in engineering practice, 3 edn. Wiley,

New York

Vidal H (1966) La terre Armee. Annales de l’Institut Technique de Batiment et de Travaux

Publics, France

Vidal H (1969) The principle of reinforced earth. Highway research record 282:1–16

Waldron LJ (1977) Shear resistance of root-permeated homogeneous and stratified soil. Proc Soil

Sci Soc Am 41(5):843–849

References 21

Chapter 2

Basic Description of Fibre-Reinforced Soil

2.1 Introduction

Fibre reinforcement in soils can be observed in nature. In our day-to-day life, you

may notice that the roots of vegetation (natural fibres) stabilize the near-surface soil

that has low shear strength, mainly because of low effective stress, on both level and

sloping grounds. Figure 2.1 shows how the fibres of different sizes (smaller than

1 mm to larger than 70 mm) as the roots of a tree strengthen the foundation soil for

its long-term stability. The presence of plant roots is a natural means of incorpo-

rating randomly distributed fibre inclusions within the soil mass. The root fibres

improve the strength of soil and the stability of soil foundations and slopes. With

learning from the root reinforcements, the fibre reinforcement concept has also

become significant in engineering construction practice. In fact, the soil strength-

ening/stabilizing/reinforcing effects of the natural fibres as the roots of vegetation

may be replicated artificially by including different types of natural and synthetic

fibres or as fibres from waste materials such as used plastic materials and old tyres

(which pose challenging environmental and disposal problems) within the soil

mass. In construction works, fibres are generally mixed randomly with soil,

resulting in randomly distributed fibre-reinforced soil (RDFRS), which is often

simply called the fibre-reinforced soil (FRS), as explained in Sect. 1.4 of Chap. 1. Insome cases, materials like cement, lime, fly ash or bituminous products are also

added to the soil along with fibres for achieving additional improvement in the

engineering properties of soil. Note that fibres are a form of structural reinforce-

ment, and their main role is working as a tension member to improve the strength

characteristics of soil in addition to their roles in influencing other properties of soil

(e.g. permeability, compressibility, etc.).

This chapter presents the basic description of fibres and fibre-reinforced soils,

focusing on types of fibres and their characteristics, and phase concept of fibre-

reinforced soil mass. Brief details of the soil reinforced with continuous fibres and

multioriented inclusions are also provided.



23

http://dx.doi.org/10.1007/978-981-10-3063-5_1

2.2 Fibres

A fibre is a unit of matter characterized by flexibility, fineness and a high ratio of

length to thickness (or diameter) (Fig. 2.1). In this book, the fibre has been

considered a general term that refers to all filaments, yarns, staples, bristles/hairs,

buffings, chips, crumbs and other similar highly flexible entities. A filament is an

untwisted individual fibre and can be crimped or uncrimped. A yarn refers to a

bundle or series of filaments twisted to produce a single fibre in which the

Fig. 2.1 Foundation soil

reinforced randomly with

natural root fibres (visible in

an excavated trench closer

to the tree) supporting a tree

24 2 Basic Description of Fibre-Reinforced Soil

individual filaments cannot be separated. Crimping of filaments helps prevent

filament separation when the yarn is made. A staple is a cut length of fibre,

measured and expressed in millimetres.

The ratio of length L to thickness (or equivalent diameter) D of the fibre is called

the aspect ratio ar. Thus

ar ¼ L

Dð2:1Þ

Fibres are obtained from natural, synthetic and waste (nonhazardous type)

materials, and therefore, they may be categorized into the following three types:

• Natural fibres (Fig. 2.3)

• Synthetic fibres (Fig. 2.4)

• Waste fibres (Fig. 2.5)

In addition to coir and jute fibres, as shown in Fig. 2.3, there are several other

natural fibres, such as wood chips, bamboo fibres, sisal fibres, palm leaves, grasses,

banana fibres, corn stalks, oat and flax straws, manila fibres, cotton fibres, etc. They

are available locally in different places worldwide, and can be used as the geofibres.

Human and animal hairs are also available as natural fibres. Most natural fibres

L

DFig. 2.2 Geometrical

dimensions of a typical fibre

Fig. 2.3 Natural fibres: (a) coir fibres, (b) jute fibres

2.2 Fibres 25

originate from plant and vegetation, animal and mineral sources. Bamboo grids and

mats are also used as soil reinforcement to create systematically reinforced soils as

the geosynthetic reinforcements are used.

Of most natural fibres, coir has the greatest tensile strength and retains this

property even in wet conditions. It is a biodegradable organic fibre material

containing 40% lignin and 54% cellulose (Rao and Balan 2000). The high content

of lignin, which is a complex hydrocarbon polymer, makes the coir fibres degrading

slowly, and so they are useful in different applications, as discussed in Chap. 5. The

coir fibres may play their roles for a long period (1–2 years) when included within

the soil mass, even in saline environment. Bamboo fibres are very strong in tension

but have low modulus of elasticity and high water absorption. The best quality of

bamboo fibres is that they are seldom eaten by pests or infected by pathogens.

Certain fibres, such as sisal fibres, have very high initial tensile strength and are

strong as the equivalent polyester fibres.

Table 2.1 provides the values of some specific properties of coir, jute and bamboo

fibres, determined by Biswas et al. (2013), using a mini-tensile/compression testing

machine, but these values contradict the observations reported in the fibre-reinforced

Fig. 2.4 Synthetic fibres: (a) polypropylene (PP) fibres, (b) glass fibres

Fig. 2.5 Waste fibres: (a) old/used tyre fibres, (b) waste/used plastic fibres


http://dx.doi.org/10.1007/978-981-10-3063-5_5

soil literature. This demonstrates that for any project work, the tabulated values of

fibres may not be the realistic values for their direct use in design of fibre-reinforced

soil structures. The properties of fibres, therefore, should be determined by

conducting the tests on the fibres being used in the project, as the fibres can vary

significantly in their properties even for the fibres coming from the same natural

plant.

Natural fibres have affordable cost, strength, environmentally friendly charac-

teristics (e.g. contributing to greener Earth by reducing the greenhouse gas emis-

sions in construction) and bulk availability, but they have some practical drawbacks

such as reproducibility and biodegradability. In addition, the fibre geometry varies

significantly, thus the design procedure with application of natural fibres may

require a special attention. Except coir fibre, most natural fibres have a poor

resistance to alkaline environment.

Natural fibres exhibit progressive loss of strength and other characteristics when

included within the soil mass. The rate of loss of property varies with type of fibres.

The problem of biodegradability of geonaturals can be overcome by suitable

treatment methods, such as alkali and other chemical treatments, enzyme treatment,

UV grafting with monomers, physical and chemical coatings using synthetic poly-

mers or resins, antimicrobial finishing, etc., with some additional cost. Thus, the

natural fibres can be used as an alternative low-cost reinforcing materials or

admixtures for improving the engineering behaviour of weak soils or other similar

materials in some field applications, such as construction of pavements for village

and forest areas, or at least in the short-term applications, such as erosion control,

where strength durability of fibres is not an issue. The use of natural fibres for

erosion control is a sustainable and environmentally friendly application.

Figure 2.4 shows only two types of synthetic fibres (PP fibres and glass fibres),

but there are several others, such as polyester (PET) fibres, polyethylene (PE) fibres,

nylon/polyamide (PA) fibres, carbon fibres, steel/metal fibres, etc. There are several

environmental factors that affect the durability of polymers. Ultraviolet component

of solar radiation, heat and oxygen and humidity are the factors above the ground

that may lead to degradation. Below the ground, the main factors affecting the

durability of polymers are soil particle size and angularity, acidity/alkalinity, heavy

metal ions, presence of oxygen, water content, organic content and temperature.

The resistance of commonly used polymers to some environmental factors is

Table 2.1 Physical/mechanical properties of some fibres

Fibre types

Tensile strength

(MPa)

Young’s modulus of elasticity

(MPa)

Strain at failure

(%)

Coir

(brown)

165–222 3.79 41.0

Coir (white) 185–237 3.97 38.7

Jute 331–414 28.43 2.6

Bamboo 615–862 35.45 4.1

After Biswas et al. (2013)

2.2 Fibres 27

compared in Table 2.2. The basic properties of these polymers are given in

Table 2.3. It must be emphasized that the involved reactions are usually slow and

can be retarded even more by the use of suitable additives. When the polymers are

subjected to a higher temperature, they lose their weight. What remains above

500 �C is probably carbon black and ash (Fig. 2.6).

The PP fibres have been widely used in experimental investigations of fibre-

reinforced soils. The primary attraction is that of low cost. It is easy to mix PP fibres

with soil, and they have relatively a high melting point, which makes it possible to

place the fibre-reinforced soil in the oven and conduct the water content determi-

nation tests. Also, the PP is a hydrophobic and chemically inert material which does

not absorb or react with the soil moisture or leachate. The fibres are produced in

fibrillated bundles. If the fibres are added to the soil during mixing cycle, the mixing

action opens the bundles and separates them into multifilament fibres (Miller and

Rifai 2004).

Synthetic fibres have the following two advantages over natural fibres (Krenchel

1973; Hoover et al. 1982):

Table 2.2 A comparison of the resistance of some polymers

Influencing factors

Resistance of polymers

PP PET PE PA

Ultraviolet light (unstabilized) Medium High Low Medium

Ultraviolet light (stabilized) High High High Medium

Alkalis High Low High High

Acids High Low High Low

Salts High High High High

Detergents High High High High

Heat, dry (up to 100 �C) Medium High Low Medium

Steam (up to 100 �C) Low Low Low Medium

Hydrolysis (reaction with water) High High High High

Micro-organisms High High High Medium

Creep Low High Low Medium

Adapted from John (1987) and Shukla (2002)

Table 2.3 Typical properties of polymers

Polymers

Specific

gravity

Melting

temperature

(�C)Tensile strength at

20 �C (MPa)

Modulus of

elasticity (GPa)

Strain at

break (%)

PP 0.90–0.91 160–165 400–600 1.3–1.8 10–40

PET 1.22–1.38 260 800–1200 12–18 8–15

PE 0.91–0.96 100–135 80–600 0.2–1.4 10–80

PVC 1.38–1.55 160 20–50 2.7–3 50–150

PA 1.05–1.15 220–250 700–900 3–4 15–30

After Shukla (2016)


1. Synthetic fibres can be produced according to desired specifications. For exam-

ple, geometry of fibres can be controlled and shape of fibres and surface

conditions can be altered in order to enhance the frictional properties of fibres.

2. Most synthetic fibres do not biodegrade when subjected to variable environ-

ments of moisture, heat, cold or sunlight.

Old/used tyres and waste plastic materials are available in large quantities

worldwide; they may be utilized in construction projects in various forms, espe-

cially in the granular form, chips or fibres; otherwise they may occupy a large

volume of the landfills when disposed of. The type of the tyre chips and fibres

depends primarily on the design of the shredder (i.e. machine for cutting). The

average specific gravity of tyre chips/fibres typically ranges from 1.13 to 1.36

(average value of 1.22) depending on the metal content. The tyre chips/fibres

without metal have a narrow range of specific gravity around 1.15. The unit weight

of pure tyre chip fills typically ranges from 3 to 6 kN/m3 (Edil and Bosscher 1994).

Tyre buffings, also called the rubber fibres, are a by-product of the tyre retread

process. They have an elongated fibrous shape with variable length of even dust size

and high strength and extensibility, and so they can be used as soil reinforcement.

Utilization of waste fibres, including some waste natural fibres (e.g. human and

animal hairs) as soil reinforcement, can avoid the environmental and disposal

Temperature (°C)

120

100

80

60

40

20

0

Wei

ght

(%)

1000 200 300 400 500 600 700 800

PVCPP

PE

PET

Fig. 2.6 Effect of temperature on some geosynthetic polymers (After Thomas and Verschoor

1988)

2.2 Fibres 29

problems. Additionally the use of waste fibre reinforcement helps in sustainable

development of various infrastructures developed on weak and unsuitable soils.

In the area of fibre composites, fibres are also classified based on their length as

(Agarwal and Lawrence 1980; Hoover et al. 1982) short fibres and continuous

fibres. The fibres smaller than 76.2 mm (3 in.) are usually called the short fibres.

The fibres longer than 76.2 mm (3 in.) when included in matrix material (e.g. soil)

extend throughout the material mass, and so they are called the long/continuous

fibres. The mechanics of stress transfer differs in composites reinforced with short

and continuous fibres. For short fibre-reinforced composite, the applied stresses are

first transferred to the matrix material, then to the fibres through the fibre ends and

the surfaces of the fibres near the fibre ends. For continuous fibre-reinforced

composite, the applied stresses are transferred to the fibres and matrix (soil) at the

same time. Details of the soil mass reinforced with almost infinite length of fibres

are briefly presented in Sect. 2.2. This book has mainly focused on presenting the

fundamentals of soil reinforced with short, discrete, flexible fibres, as they have

been studied and their applications have been reported, without strictly following

the upper length limit for short fibres as classified in the area of fibre composites.

Basic properties of fibres used for reinforcing the soils in several laboratory and

field studies of fibre-reinforced soils are given in Table 2.4.

The following points regarding fibres are worth mentioning:

1. A long continuous roll of a single filament, groups of filaments or yarns is

called the tow.

2. Fibres can be either straight or crimped (texturized). Crimping is one of the

texturing procedures for fibres.

3. In the fibre industry, the fibres are also described in terms of linear mass density

(kg/m), which is generally expressed in denier (grams per 9 km of the fibre) or

tex (grams per 1 km of the fibre). Thus, 1 denier ¼ 1 g/9 km, 1 tex ¼ 1 g/ km,

and 1 tex ¼ 9 denier.

4. Denier is an indirect measure of fibre diameter. For example, if 9 km of PET

filaments weighs 120 g, it is classed as a 120-denier filament.

5. It is possible to convert denier to more conventional diametric measure by

relating denier to specific gravity through the volumetric relation for a circular

cylinder. As an example, a 75-denier filament would have a diameter

corresponding to a fine-textured human hair, while a 2500-/250-denier yarn

would correspond in size to a packing twine. A 2500/250 yarn of fibre denotes a

fibre with a 2500 total denier measure but composed of 250 individual fila-

ments, each of which is 10 denier (Hoover et al. 1982).

6. The fibre properties, such as tensile strength, tensile modulus, elongation/strain

at break, tenacity, etc., are based on the denier of the fibre.

7. Tenacity is a measure of the tensile strength of a fibre expressed in terms of

grams/denier. A 100-denier filament that breaks under a 250-g load is rated at

2.5 g/denier. Elongation at break refers to strain characteristic of the fibre, i.e. a

measure of longitudinal deformation that occurs prior to rupture, and expressed

as a percentage (Hoover et al. 1982).


Table

2.4

Properties

offibres

Characteristics

offibres

Kaniraj

and

Havanagi

(2001)

Consoli

etal.

(2009)

Jha

etal.

(2015)

Park

(2009)

Spritzer

etal.

(2015)

Lovisa

etal.

(2010)

Khattakand

Alrashidi

(2006)

Babu

etal.

(2008)

Spritzer

etal.(2015)

Sarbaz

etal.

(2014)

Type

PETfibres

PPfibres

PE

fibres

PVA

fibres

Nylon

fibres

Glass

fibres

PCfibres

Coir

fibres

Jute

fibres

Date

palm

fibres

Specificgrav-

ity,Gf

1.3

0.91

0.99

1.3

1.15

1.7

1.5

1.07

1.47

0.92

Averagelength,

L(m

m)

20

24

12

12

6–18

10–15

315

7–9

295

Equivalent

diameter,

D(m

m)

0.075

0.023

0.035

0.1

0.003–0.01

0.02

0.015

0.25

0.005–0.025

0.42

Tensilestrength

σf(M

Pa)

80–170

120

600

1078

300

300

500

102

331–414

123

Strainat

break/

failure

(%)

80

5.10

Tensile

modu-

lus,Ef(G

Pa)

1.45–2.5

350

22.47

Note:PETpolyester,PPpolypropylene,PEpolyethylene,PVApolyvinylalcohol,PCprocessed

cellulose

(derived

from

processingofwood)

2.2 Fibres 31

8. Steel fibres are prone to rust and acids. Glass fibres are expensive.

9. Natural fibres lose their strength when subjected to alternate wetting and drying

environment. They are environmentally friendly construction materials.

10. What part of the plant the fibres come from, the age of the plant, and how the

fibres are isolated are some of the factors which affect the performance of

natural fibres in a natural fibre-reinforced soil (Rowell et al. 2000).

Example 2.1

Determine the aspect ratio of the PP fibres if their average length and diameter are

20 mm and 0.05 mm, respectively.

Solution

Given: L¼ 20 mm and D¼ 0.05 mm

From Eq. (2.1), the aspect ratio,

ar ¼ L

D¼ 20

0:05¼ 400

2.3 Phases in a Fibre-Reinforced Soil Mass

Fibres can be considered similar to soil solid particles. Hence, like an unreinforced

soil mass, the fibre-reinforced soil mass may be represented by a three-phase system

as shown in Fig. 2.7, with fibre and soil solids represented separately. The concept

of phase relationships, being adopted widely in soil mechanics (Shukla 2014) and

geotechnical engineering (Shukla 2015) for unreinforced soils, can be utilized for

developing the phase relationships for fibre-reinforced soils. Some phase relation-

ships for the fibre-reinforced soils are defined below:

Void ratio of the soil mass only,

Air/gas

Soil solid Air/gas

Water/liquid

V

vVwV

aV

ssV

0a ≈W

W

wW

ssW

Water/liquid

Fibre solid

Soil solidsW

sfWsfV

sV

Fibre solida b

Fig. 2.7 An element of fibre-reinforced soil mass: (a) phases in the natural state, (b) phases

separated for mathematical analysis


es ¼ Vvs

Vss

ð2:2Þ

Void ratio of the fibre mass only,

ef ¼ Vvf

Vsf

ð2:3Þ

Void ratio of the fibre-reinforced soil mass,

eR ¼ Vv

Vs

ð2:4Þ

Volume ratio of the fibre-soil solids,

Vr ¼ Vsf

Vss

ð2:5Þ

where Vvs is the volume of soil voids, Vss is the volume of soil solids, Vvf is the

volume of fibre voids, Vsf is the volume of fibre solids, Vv(¼Vvs +Vvf¼Va +Vw) is

the volume of voids of fibre-reinforced soil and Vs(¼Vss +Vsf) is the volume of

solids of fibre-reinforced soil.

Note that in Fig. 2.7, the subscripts a, w, v and f refer to air, water, void and fibre,

respectively. In symbols with dual subscripts, the subscript s when appears first

refers to ‘solid’ but it refers to ‘soil mass’ when appears as the second subscript.

The following terms are often used to describe the behaviour of fibre-reinforced

soils:

Fibre content (a.k.a concentration of fibres or weight ratio or weight fraction or

gravimetric fibre content),

pf ¼Wsf

Wss

ð2:6Þ

Fibre area ratio,

Ar ¼ Af

Að2:7Þ

Volumetric fibre content,

pvf ¼Vsf

Vð2:8Þ

whereWss is the weight of soil solids (i.e. dry weight of soil,Wds),Wsf is the weight

of fibre solids (i.e. dry weight of fibres, Wdf), Af is the total cross-sectional area of

2.3 Phases in a Fibre-Reinforced Soil Mass 33

fibres in a plane (e.g. shear/failure plane) of area A within the reinforced soil mass

and V is the total volume of the fibre-reinforced soil element.

The following points are worth mentioning:

1. In the denominator of Eq. (2.6), the weight of soil solids is used instead of the

weight of fibre-reinforced soil solids for maintaining the consistency with soil

mechanics practice as the water content is defined. This practice is often

followed in stabilization of soil with admixtures such as cement, lime and fly

ash. For example, the cement content pc in cement-stabilized soil is defined as

pc ¼Wsc

Wss

ð2:9Þ

where Wsc is the weight of cement solids (i.e. dry weight of cement, Wdc).

2. In the case of cement-stabilized fibre-reinforced soil, the fibre content may be

defined as

pf ¼Wsf

Wss þWsc

ð2:10Þ

3. The values of pf, pvf, Ar and pc are normally expressed as a percentage (%).

4. If the fibres are oriented perpendicular to the failure plane in any specific

application, Ar¼ pvf.5. It is easier to measure pf than pvf. Hence, for practical purposes, such as

preparation of test specimens of fibre-reinforced soil and its field applications,

pf is conveniently used. The use of pvf is often done in modelling of fibre-

reinforced soils based on theory of mixtures because the mechanical properties

of the composite constituents (soil and fibres), especially when the unit weights

of the constituents differ greatly, are governed significantly by the volumetric

parameters, and they are not necessarily related to the unit weights (Michalowski

and Zhao 1996).

From Eq. (2.8),

pvf ¼Vsf

V¼ V � Vss þ Vvð Þ

V¼ 1� Vss þ Vv

V¼ 1� pvs ð2:11Þ

where pvs is the volumetric soil content in fibre-reinforced soil. Thus

pvs ¼Vss þ Vv

Vð2:12Þ

and

pvs þ pvf ¼ 1 ð2:13Þ


The parameters pvs and pvf are also known as volumetric concentration factors for

the soil matrix and fibres, respectively. These factors are used in the development of

constitutive models for the fibre-reinforced soil (Ibraim et al. 2010). Note that in the

definition of pvs, the volume of voids Vv, excluding the part occupied by the fibres,

is considered to be the part of the volume of soil matrix.

Using a mixture rule, the effective stress σ0R within the fibre-reinforced soil can

be divided into soil matrix and fibre matrix components as (Ibraim et al. 2010):

σ0R ¼ pvsσ0 þ pvfσ

0f ð2:14Þ

where σ0 is the effective stress of the soil matrix and σ0f is the effective stress of thefibre matrix. For an unreinforced soil, pvf¼ 0, pvs¼ 1 and σ0R ¼ σ0, which representsthe effective stress for soil only in a conventional way as per the Terzaghi’seffective stress concept.

One can develop useful phase interrelationships in view of their practical

applications as we do in soil mechanics. Several researchers have considered the

phase concept and used specific phase relationships and interrelationships while

analysing the behaviour of fibre-reinforced soils as required in their investigations.

For example, Maher and Gray (1990) considered fibres to be a part of solid fraction

of fibre-reinforced soil with different specific gravity from that of soil solids in their

study as considered in Fig. 2.7. Shukla et al. (2015) presented the following phase

interrelationships:

eR ¼ es þ Vref1þ Vr

ð2:15Þ

Vr ¼ pfG

Gf

ð2:16Þ

eR ¼ GRγwγdR

� 1 ð2:17Þ

GR ¼ 1þ pfð Þ 1

Gþ pfGf

� ��1

ð2:18Þ

where γw is the unit weight of water, G is the specific gravity of soil solids, Gf is the

specific gravity of fibre solids, GR is the specific gravity of fibre-reinforced soil

solids and γdR is the dry unit weight of fibre-reinforced soil.

Referring to Fig. 2.7, the expression for γdR is given as

γdR ¼ Wsf þWss

V¼ Ws

Vð2:19Þ

From Eqs. (2.6), (2.8) and (2.19),


pvf ¼pfγdR

1þ pfð ÞGfγwð2:20Þ

or

pf ¼Gfγwpvf

γdR � Gfγwpvf¼ 1

γdRGfγwpvf

� 1ð2:21Þ

Using Eqs. (2.17) and (2.18), Eq. (2.20) becomes

pf ¼1þ eRð ÞGfpvf

G 1� 1þ eRð Þpvf½ � ð2:22Þ

Example 2.2

Derive the expressions given in Eq. (2.15) and (2.16).

Solution

Derivation of Equation (2.15):

eR ¼ Vv

Vs

(using Eq. (2.4))

¼ Vvs þ Vvf

Vss þ Vsf

(Void volume occupied by air and/or water may be considered to be contributed by

soil solids and fibre solids separately.)

¼Vvs

Vssþ Vsf

Vss� Vvf

Vsf

1þ Vsf

Vss

(dividing numerator and denominator by Vss)

¼ es þ Vref1þ Vr

(using Eqs. (2.2), (2.3) and (2.5))

Derivation of Equation (2.16):

Vr ¼ Vsf

Vss


(using Eq. (2.5))

¼ Wsf=γwGfð ÞWss=γwGð Þ

,G ¼ Wss=Vss

γwand Gf ¼ Wsf=Vsf

γw

� �

¼ WsfG

WssGf

¼ pfG

Gf

(using Eq. (2.6))

Example 2.3

If a clayey soil is reinforced with 1.25% of PET fibres, determine the specific

gravity of the fibre-reinforced soil. Assume the specific gravity values for soil solids

and fibre solids are 2.70 and 1.3, respectively.

Solution

Given: pf¼ 1.25%, G¼ 2.70, and Gf¼ 1.3

From Eq. (2.18), the specific gravity of fibre-reinforced soil is

GR ¼ 1þ pfð Þ 1

Gþ pfGf

� ��1

¼ 1þ 0:0125ð Þ 1

2:70þ 0:0125

1:3

� ��1

¼ 2:66

Note that the phase relationships and interrelationships, as presented here, are

fairly of general nature and can be utilized in several applications of fibre-

reinforced soils in a way similar to that traditionally used in soil mechanics and

geotechnical engineering for the analysis of unreinforced soils. Based on the

laboratory experiments, Shukla et al. (2015) presented the variation of void ratio

eR of the fibre-reinforced sand with logarithm of (100Vr + 1), as shown in Fig. 2.8,

with the following empirical expression:

eR ¼ aln 100Vr þ 1ð Þ þ b ð2:23Þ

where a¼ 0.0333 is the slope of the linear relationship and represents the type of

fibre used (i.e. virgin homopolymer polypropylene) and b¼ 0.4913 is the value of

eR at Vr¼ 0 and represents the type of sand used (i.e. poorly graded silica sand). For

other types of fibre and/or sand, a and b can be obtained from the data obtained from

a minimum of four compaction tests on the fibre-reinforced soil at hand from which

the measured values of Vr and the corresponding eR can be calculated and used to

determine a and b, then the equation similar to Eq. (2.23) can be used for future

prediction of the void ratio of the specific fibre-reinforced soil.

The coefficient of determination R2 of the correlation in Eq. (2.23) is 0.9935.

Note that R2 is an index of the reliability of the relationship. A regression equation


that lies close to all the observation points gives a higher value of R2. The maximum

value of R2 is unity. A suitable numerical software package, such as MATLAB, is

generally used for developing the statistical relationships between two or more

variables. Such relationships are called the statistical or regression models. A few

more regression models are presented in Chap. 4.

It is expected that the researchers may carry out experimental studies with

several types of fibre and soil and also with cemented fibre-reinforced soils to

compare their results with the phase relationships as presented here and also

develop similar new expressions as required for their use by practicing engineers.

2.4 Soil Reinforced with Continuous Fibres

and Multioriented Inclusions

The soil can be reinforced randomly with continuous fibres or multioriented

(3-dimensional, 3D) inclusions. Some studies are available for such reinforced soils.

The sand reinforced with continuous synthetic (PET, PP, etc.) fibres/threads was

originally conceived by Laboratoire Central des Ponts et Chaussees (LCPC) and

registered as Texsol (Leflaive 1982). To obtain the soil reinforced with continuous

fibres, a number of threads are pneumatically or hydraulically projected on sand in a

movement at the extremity of a conveyor belt or at the vent of a pipe used to build a

hydraulic fill at the construction site. A special machine was designed to produce up

to 20 m3/h of Texsol with the use of about 100 km/m3 of thread, projected

1 001010.48

0.50

0.52

0.54

0.56

0.58

0.60

1100 r +V

eR

Fig. 2.8 Variation of void ratio eR of the fibre-reinforced sand with logarithm of (100Vr + 1)

(Adapted from Shukla et al. 2015)


http://dx.doi.org/10.1007/978-981-10-3063-5_4

simultaneously from 50 bobbins at the speed of 10 m/s (Leflaive et al. 1983; Prisco

and Nova 1993).

In the thread-reinforced soil, the sand particles and threads are closely connected

because of friction between them, and hence the threads react in tension to any

extensional deformation caused by loading, thus giving an artificial confinement to

sand. As a consequence, both strength and stiffness of sand in the presence of

threads increase (Prisco and Nova 1993). The fibre content typically varies between

0.1 and 0.2%. The triaxial compression tests on thread-reinforced sand shows that

significant cohesions of the order of 200 kPa for 0.2% fibre content by weight of

sand may result. The angle of internal friction of reinforced sand is, however,

essentially the same as that of unreinforced sand. Note that the way in which

such a material is put in place gives the reinforced soil an ordered structure, so

that the measured cohesion and friction angle vary with the orientation of the

bedding plane with respect to the principal axes of stress (Leflaive and Liausu

1986; Prisco and Nova 1993). Failure normally occurs at strains larger than those of

unreinforced sand. Thus, the thread-reinforced soil is more ductile than sand and

can be considered essentially as a cemented soil. To achieve the full strength of

thread-reinforced soil, significant strains and consequently significant deformations

may take place; this may not be a desirable characteristic for some applications,

such as the use of thread-reinforced soil to support structural loads as a foundation

bed. The design of structures constructed with thread-reinforced soils can be based

on limit equilibrium methods when the strains/deformations are limited. Numerical

and constitutive models have also been presented for the analysis of such reinforced

soils (Villard and Jouve 1989; Prisco and Nova 1993).

In the past, thread-reinforced sandy soils have been used for constructing earth

retaining walls, particularly on soft compressible soils, with facing slope angles as

high as 75�, filter or drain resistant to erosion, embankments with steep slopes,

foundation beds over compressible soils and explosion-resistant facilities in civil

and military installations for storage of explosives and liquefied gas. Thread-

reinforced soils are also used for slope stabilization works (Leflaive 1985; Khay

et al. 1990; Ishizaki et al. 1992). The thread-reinforced soils provide a suitable

environment for vegetation to grow on the reinforced soil structures, and they are

also effective to resist dynamic loads.

The soil can be strengthened by inclusion of multioriented/3D geosynthetic

elements (termed jacks) within or upon a compacted or naturally deposited granular

soil (Lawton and Fox 1992; Lawton et al. 1993). These elements can be oriented

randomly within a compacted soil mass by mixing them with soil prior to compac-

tion; placed in layers on lifts of loose soil, compacted soil or naturally deposited soil

layer; or placed in a layer on the surface of a naturally deposited soil or compacted

fill and pressed into the soil by compaction. 3D elements can also be used as

lightweight, highly porous artificial soil.

A large number of 3D elements of different sizes and shapes are available, and

they can also be designed to meet specific requirements of the project. Lawton et al.

(1993) used five types of 3D inclusions in their research. All 3D elements consisted

of six stems extending radially from a central hub, with enlarged heads on four of

2.4 Soil Reinforced with Continuous Fibres and Multioriented Inclusions 39

the stems, but they differed in material and manufacturing process. Both layered

and random oriented inclusions are effective in strengthening and/or stiffening the

granular soil under certain conditions. Increases in deviator stress at failure as large

as above 100% can be determined in triaxial tests. Additional details about behav-

iour of soils with 3D inclusions can be found in the works of Zhang et al. (2006) and

Harikumar et al. (2016).

Chapter Summary

1. A fibre is a unit of matter characterized by flexibility, fineness and a high ratio

of length to thickness (or diameter). In general, the fibre is a general term that

refers to all filaments, yarns, staples, bristles/hairs, buffings, chips, crumbs and

other similar highly flexible entities.

2. Fibres available for use in construction can be classified as natural fibres

(e.g. coir fibres, jute fibres, etc.), synthetic fibres (e.g. polypropylene fibres,

polyester fibres, etc.) andwaste fibres (old/used tyre fibres, used plastic fibres, etc.).

3. The PP fibres have been widely used in experimental investigations of fibre-

reinforced soils. The primary attraction is that of low cost.

4. In the fibre industry, the fibres are also described in terms of linear mass density

(kg/m), which is generally expressed in denier (grams per 9 km of the fibre) or

tex (grams per 1 km of the fibre).

5. An element of fibre-reinforced soil can be represented as a three-phase system

consisting of solid, liquid and gas phases.

6. Fibre aspect ratio, fibre content, fibre area ratio and volumetric fibre content are

commonly used parameters in the fibre-reinforced soil engineering.

7. There are several phase relationships and interrelationships for their use in

analysis of fibre-reinforced soils.

8. The volume ratio of fibre-soil solid is uniquely related to the void ratio of the

fibre-reinforced soil.

9. Texsol is a continuous thread-reinforced soil mass, generally created at the

construction site, as a homogeneous construction material by mixing sand and

threads in a highly specialized manner for construction of retaining walls and

some other structures.

10. Soil can be improved by 3D inclusions of different shapes and sizes as per the

requirement of the specific project.

Questions for Practice

(Select the most appropriate answer to the multiple-choice questions from Q 2.1

to Q 2.5.)

2.1 The specific gravity of glass fibres is

(a) 0.91

(b) 0.99

(c) 1.38

(d) 1.7


2.2 A 90-denier filament has a weight of

(a) 1 g/km

(b) 9 g/km

(c) 10 g/km

(d) 90 g/km

2.3 The ratio of length of a fibre to its average diameter is called

(a) Fibre content

(b) Fibre aspect ratio

(c) Fibre area ratio

(d) Volumetric fibre content

2.4 Which one of the following can be measured easily?

(a) Volumetric fibre content and aspect ratio

(b) Fibre content and volumetric fibre content

(c) Fibre content and aspect ratio

(d) Fibre content, volumetric fibre content and aspect ratio

2.5 In soil reinforced with continuous fibres, the fibre content typically varies

between

(a) 0.1% and 0.2%

(b) 0.5% and 1%

(c) 1% and 2%

(d) 2% and 4%

2.6 Classify the available fibres on the basis of their sources.

2.7 What are the favourable and unfavourable characteristics of natural fibres?

2.8 Polypropylene (PP) fibres have been used widely for reinforcing soil in

research works. Can you explain the reasons?

2.9 Compare the resistances of PP and PET fibres against the following: UV light,

acids, alkalis and heat.

2.10 Compare the specific gravity values of different fibres.

2.11 Define the following: fibre content, aspect ratio and area ratio.

2.12 How is cement content in cement-stabilized soils defined? What are the two

different ways of defining fibre content in cement-stabilized soils?

2.13 Develop a relationship between volumetric soil content and volumetric fibre

content.

2.14 Write an expression for the effective stress within a fibre-reinforced soil mass.

2.15 Derive the following expressions in which the symbols have their usual

meanings:

að Þ eR ¼ GRγwγdR

� 1

bð Þ GR ¼ 1þ pfð Þ 1

Gþ pfGf

� ��1

2.4 Soil Reinforced with Continuous Fibres and Multioriented Inclusions 41

2.16 If a sandy soil is reinforced with 1% of PP fibres, determine the specific

gravity of the fibre-reinforced soil. Assume the specific gravity values for soil

solids and fibre solids are 2.65 and 0.91, respectively.

2.17 For a fibre-reinforced soil, the following details are available:

Fibre content, pf¼ 0.75%

Specific gravity of soil solids, G¼ 2.66

Specific gravity of fibre solids, Gf¼ 0.99

Determine the volume ratio of fibre-soil solids, Vr.

2.18 For a PP fibre-reinforced poorly graded sand, compacted at its maximum dry

unit weight, the volume ratio of fibre-soil solids, Vr¼ 5%. Estimate the void

ratio of fibre-reinforced sand.

2.19 What is Texsol? List its different applications. Do you expect any difficulty in

construction?

2.20 Collect the information about different multidirectional inclusions, which are

available in your local area, for soil improvement purpose. How do these

inclusions differ from short, discrete fibres?


2.1 (d)

2.2 (c)

2.3 (b)

2.4 (c)

2.5 (a)

2.16 2.60

2.17 2%

2.18 0.545

References

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New York

Babu GLS, Vasudevan AK, Haldar S (2008) Numerical simulation of fibre-reinforced sand

behaviour. Geotext Geomembr 26(2):181–188

Biswas S, Ahsan Q, Cenna A, Hasan M, Hassan A (2013) Physical and mechanical properties of

jute, bamboo and coir natural fibres. Fibers Polym 14(10):1762–1767

Consoli NC, Casagrande MDT, Thome A, Rosa FD, Fahey M (2009) Effect of relative density on

plate loading tests on fibre-reinforced sand. Geotechnique 59(5):471–476

Edil TC, Bosscher PJ (1994) Engineering properties of tire chips and soil mixtures. Geotech Test J

17(4):453–464

Harikumar M, Sankar N, Chandrakaran S (2016) Behaviour of model footing resting on sand bed

reinforced with multidirectional reinforcing elements. Geotext Geomembr 44(4):568–578




Project Report HR-211. Department of Civil Engineering, Engineering Research Institute,

Iowa State University, Ames, USA

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under monotonic loading. Geotext Geomembr 28(4):374–385

Ishizaki H, Tanabe D, Segawa S (1992) Application of the continuous fibre – soil reinforcement

method to the construction of a permanent retaining wall. In: Proceedings of Seiken sympo-

sium on recent case histories of permanent geosynthetic-reinforced soil retaining walls, Tokyo,

Japan, pp 223–226

Jha JN, Gill KS, Choudhary AK, Shukla SK (2015). Stress-strain characteristics of fiber-reinforced

rice husk ash. In: Proceedings of the Geosynthetics 2015, Portland, OR, USA, pp 134–141

John NWM (1987) Geotextiles. Blackie, London

Kaniraj SR, Havanagi VG (2001) Behaviour of cement-stabilized fiber-reinforced fly ash-soil

mixtures. J Geotech Geoenviron Eng ASCE 127(27):574–584

Khattak MJ, Alrashidi M (2006) Durability and mechanistic characteristics of fiber reinforced soil

– cement mixtures. Int J Pavement Eng 7(1):53–62

Khay M, Gigan JP, Ledelliou M (1990) Reinforcement with continuous thread: technical devel-

opments and design methods. In: Proceedings of the 4th international conference on

geotextiles, geomembranes and related products, The Hague, vol 1, pp 21–26

Krenchel H (1973) Fiber reinforced brittle matrix materials. In: Proceedings of international

symposium on fiber reinforced concrete, Ottawa

Lawton EC, Fox NS (1992) Field experiments on soils reinforced with multioriented geosynthetic

inclusions. Transp Res Rec 1369:44–53

Lawton EC, Khire MV, Fox NS (1993) Reinforcement of soils by multioriented geosynthetic

inclusions. J Geotech Eng ASCE 119(2):257–275

Leflaive E (1982) The reinforcement of granular materials with continuous fibers. In: Proceedings

of the second international conference on geotextiles, Las Vegas, USA, pp 721–726

Leflaive E (1985) Soil reinforced with continuous yarns: Texol. In: Proceedings of 11th interna-

tional conference on soil mechanics and foundation engineering, San Francisco, USA, vol 3, pp

1787–1790

Leflaive E ,Liausu Ph (1986) Le renforcement des sols par fil continus. In: Proceedings of the third

international conference on geotextiles, Vienna, pp 523–528

Leflaive E, Khay M, Blivet JC (1983) Le Texsol. Bull Liaison LCPC 15:105–114

Lovisa J, Shukla SK, Sivakugan N (2010) Shear strength of randomly distributed moist fiber-

reinforced sand. Geosynth Int 17(2):100–106

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Geotech Eng ASCE 116(11):1661–1677

Michalowski RL, Zhao A (1996) Failure of fiber-reinforced granular soils. J Geotech Eng ASCE

122(3):226–234

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ASCE 130(8):891–895

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of fiber-reinforced cemented sand. Geotext Geomembr 26(2):162–166

Prisco CD, Nova R (1993) A constitutive model for soil reinforced by continuous threads. Geotext

Geomembr 12(2):161–178

Rao GV, Balan K (2000) Coil geotextiles – emerging trends. Kerala State Coir Corporation

Limited, Alappuzha

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Polym Agrofibers Compos:115–134

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and considering environmental factors. Int J Pavement Eng 15(7):577–583

Shukla SK (2002) Geosynthetics and their applications. ICE Publishing, London


Shukla SK (2015) Core concepts of geotechnical engineering. ICE Publishing, London


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Geosyn Ground Eng Switz 1(3):29.1–29.5

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dewatering rate and shear strength of slurries in geotextile tube applications. Int J Geosyn

Ground Eng 1(3):26.1–26.14

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(3):24–30

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Comput Geotech 7(1–2):83–98

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Geomembr 24(4):201–209


Chapter 3

Engineering Behaviour of Fibre-

Reinforced Soil

3.1 Introduction

In the early days of soil reinforcement practice, most experimental and mathemat-

ical studies considered reinforcing the soil with continuous metal and geosynthetic

reinforcement elements, such as strips, bars, discs and meshes, in a definite pattern

(e.g. horizontal, vertical and inclined orientations) for investigating the behaviour

of systematically reinforced soils. McGown et al. (1985) investigated the strength-

ening of a granular soil using randomly distributed polymeric mesh elements and

observed the improvement in strength of the soil at all strain levels, even at very

small strains. The action of randomly distributed polymeric mesh elements is to

interlock particles and groups of particles together to form a unitary, coherent

matrix. Because of the limited practical scope of random distribution of continuous

metal and geosynthetic reinforcement elements, these elements have not been used

widely for reinforcing the soils randomly, and hence the studies of such reinforced

soil systems have not been given much attention.

Over the past 30–35 years, the engineering behaviour of randomly distributed,

discrete, flexible, fibre-reinforced soils has been studied in significant details by

many researchers worldwide. Most studies are based on the laboratory and small-

scale tests, such as direct shear tests, triaxial compression tests, unconfined com-

pression tests, compaction tests, California bearing ratio (CBR) tests, plate load

tests, etc. This chapter presents the engineering behaviour of randomly distributed,

discrete, flexible, fibre-reinforced soils as investigated through these tests by focus-

ing on the key factors that govern the behaviour and test observations and their

critical analysis in view of their field applications.



45

3.2 Factors Affecting the Engineering Behaviour

Improvement in the engineering properties (strength, stiffness/modulus, permeabil-

ity, etc.) of soil by inclusion of discrete flexible fibres within the soil mass depends

on several factors relating soil characteristics; fibre characteristics; fibre concentra-

tion; distribution and orientation; type of admixtures, if any; mixing and compac-

tion methods; and test/field conditions, as listed below:

• Soil characteristics: types (cohesionless/cohesive/cohesive-frictional); particle

shape and size; gradation, generally expressed in terms of mean particle size

(D50) and coefficient of uniformity (Cu); unit weight of soil solids; total unit

weight; water content; and shear strength

• Fibre characteristics: fibre types and materials (natural/synthetic/waste); shapes

(monofilament, fibrillated, tape, mesh, etc.); fibre diameter, fibre length and

aspect ratio (length to diameter ratio); specific surface; specific gravity of fibre

solids; tensile strength, longitudinal stiffness/modulus of elasticity, linear strain

at failure; fibre texture (straight or crimped); surface roughness and skin friction

with soil; water absorption; melting point; and durability (resistance to biolog-

ical and chemical degradation)

• Fibre concentration (fibre content, fibre area ratio), distribution and orientation

• Types of admixtures, such as lime, cement, fly ash, etc., if any

• Method of mixing of fibres with soil

• Type and amount of compaction in tests and fields, as applicable

• Test and/or field conditions and variables: confining/normal stress level, rate of

loading, rate of strain, etc.

During laboratory and/or field investigations, as many of these factors/parame-

ters as possible should be varied in a scientific manner to ascertain the influence of

fibres on the engineering behaviour of soil and other similar materials when

reinforced with fibres. The complete investigation is also required to validate the

theoretical models of fibre-reinforced soils as presented in Chap. 4.

The engineering behaviour of fibre-reinforced soil, especially the strength char-

acteristics, is significantly governed by interfacial shear resistance of the fibre-soil

interface, which is affected by the following four primary parameters (Tang et al.

2007a; Gelder and Fowmes 2016): friction, bonding force, matrix suction and

interface morphologies. These primary parameters are controlled by the following

four indirect factors: water content, size effect, soil dry unit weight and cement

inclusions. As a result of load application on the fibre-reinforced soil, the soil

particles at the soil-fibre interface may have a tendency of rotation, and the fibre

in tension may undergo plastic deformation at the sharp corners/edges of the

particles. In the presence of lime or cement in soil, the rotation of particles at the

soil-fibre interface is restricted by increased bonding force due to cementation. The

hydrated product developed on the surface of the fibre increases the roughness and

penetrates the surface. Addition of lime in clay with fibres causes flocculation and

results in flocculated silt-size particles, which contact the fibre surface and help in

46 3 Engineering Behaviour of Fibre-Reinforced Soil

http://dx.doi.org/10.1007/978-981-10-3063-5_4

cementing the flocculated structure to the fibre surface, resisting rotation of parti-

cles at the interface and hence increasing the interfacial shear resistance.

3.3 Shear Strength

Shear strength of fibre-reinforced soils has been studied by carrying out both direct

shear tests and triaxial compression tests, mostly in accordance with standards

applicable to unreinforced soils. The strength behaviour of fibre-reinforced soil is

presented here as observed in these tests separately.

3.3.1 Observations in Direct Shear Tests

Based on the direct shear tests, the improvement in shear strength of soil, as a result

of inclusion of fibre reinforcement, can be expressed in terms of the shear strengthimprovement factor Is, defined as

Is ¼ ΔττfU

¼ τR � τfUτfU

¼ τRτfU

� 1 ð3:1Þ

where τfU is the shear strength of the unreinforced soil and τR is the shear stress on

the fibre-reinforced soil specimen corresponding to the shear displacement δ(¼δfU)of the unreinforced soil specimen at failure. The factor Is basically presents the

relative gain in shear strength of soil due to inclusion of fibres and is normally

expressed as a percentage.

Note that in Eq. (3.1), τR can be the shear stress on the reinforced soil specimen

at any selected/permissible shear displacement as required for the safety of the

specific structure under consideration. For τR¼ τfR (shear strength of reinforced

soil) at δ¼ δfR (shear displacement of reinforced soil specimen at failure), Eq. (3.1)

reduces to the shear strength improvement factor at failure Isf, given as

Isf ¼ ΔτfτfU

¼ τfR � τfUτfU

¼ τfRτfU

� 1 ð3:2Þ

Gray and Ohashi (1983) carried out the direct shear tests on a dry, clean, beach

sand (relative density of 20% and 100%) reinforced with natural and synthetic

fibres and metal (copper) wires (1 mm–2 mm thick, 20–250 mm long). The fibres

were always placed in a regular pattern at approximately equal spacings from each

other and from the sides of the shear box in either a perpendicular orientation to the

shear plane or at some other predetermined orientation. The experimental observa-

tions were compared with theoretical predictions based on a force-equilibrium

3.3 Shear Strength 47

model of fibre-reinforced sand, as described in Sec. 4.3.2. The test results indicate

the following:

1. Relatively low-modulus, fibre reinforcements (natural and synthetic fibres)

behave as ‘ideally extensible’ inclusions; they do not rupture during shear.

Their main role is to increase the peak shear strength and to limit the magnitude

of post-peak reduction in shear resistance in a dense sand.

2. Shear strength increases of sand are directly proportional to fibre area ratios, at

least up to 1.7%.

3. Shear strength increases as a result of fibre reinforcement are approximately the

same for loose and dense sands. However, larger strains are required to reach the

peak shear resistance in the loose case.

4. Shear strength envelopes for fibre-reinforced sand clearly show the existence of

a threshold confining stress below which the fibres tend to slip or pullout. The

strength envelops also indicate that the fibres do not affect the angle of internal

friction of the sand. Thus the fibre inclusion in sand plays their role mainly to

increase the cohesion intercept for the sand.

5. The fibres oriented either perpendicular to or randomly around the shear plane

yield approximately the same shear strength increase.

6. Shear strength increases are greatest for the fibre initial orientations of 60�with

respect to the shear surface. This orientation coincides with the direction of

maximum principal tensile strain in a direct shear test.

7. Increasing the length of fibre reinforcements increases the shear strength of the

fibre-reinforced sand, but only up to a point beyond which any further increase in

fibre length has no effect.

Kaniraj and Havanagi (2001) conducted direct shear tests at a deformation rate

of 0.25 mm/min on specimens (60 mm � 60 mm � 29 mm) of Rajghat fly ash,

Delhi silt, mixture of 50% Rajghat fly ash and 50% Delhi silt and mixture of 50%

Rajghat fly ash and 50%Yamuna sand with and without random distribution of PET

fibre reinforcement. The results show that whereas the unreinforced fly ash-soil

specimens reach their failure shear stress at displacements of 1–2 mm, the

corresponding displacements in fibre-reinforced specimens are generally more

than 4 mm and even exceed 10 mm at higher normal stresses. This is the evidence

of the fibre reinforcement imparting ductility to the unreinforced fly ash-soil

specimens. The compacted specimens show the usual tendency of dilation. How-

ever, the vertical displacement is significantly higher in the fibre-reinforced spec-

imens than in the unreinforced specimens. Table 3.1 provides the total stress-

strength parameters (cohesion intercept c and angle of shearing resistance ϕ)obtained from direct shear tests on unreinforced and fibre-reinforced soils.

In Table 3.1, you may notice that the trend in the change of c and ϕ due to fibre

inclusions is not very consistent. However, the fibre inclusions generally tend to

increase the shear strength.

The test results obtained from the direct shear tests conducted by Yetimoglu and

Salbas (2003) using a standard laboratory shear box (60 mm by 60 mm in plan and

25 mm in depth) indicate that the peak shear strength and initial stiffness of the clean,


http://dx.doi.org/10.1007/978-981-10-3063-5_4#Sec5

oven-dried, uniform river sand having particles of fine to medium size (0.075–2 mm)

at a relative density of 70% are not affected significantly by the PP fibre (length ¼20mm; diameter¼ 0.05mm) reinforcements varying from 0.10 to 1%. The horizontal

displacements at failure are also found comparable for reinforced and unreinforced

sands under the same vertical normal stress. However, the fibre reinforcements reduce

the soil brittleness providing a smaller loss of post-peak strength. Thus, there appears

to be an increase in residual shear strength angle of the sand by adding fibre

reinforcements.

Tang et al. (2007b) conducted a series of direct shear test on clayey soil cylindrical

specimens (diameter ¼ 61.8 mm, length ¼ 20 mm) with inclusion of different

percentages of PP fibres (12 mm long) and ordinary Portland cement at vertical

normal stresses of 50, 100, 200 and 300 kPa. All the test specimens were compacted

at their respective maximum dry unit weight and optimum water content. The

specimens treated with cement were wrapped with plastic membrane in the curing

box for 7, 14 and 28 days. Figure 3.1 shows the variation of shear strength parameters

(cohesion c and angle of internal friction ϕ) with fibre content. It is observed that thevalues of c andϕ increase with increasing fibre content. For the same fibre content, the

cement inclusion significantly enhances the shear strength parameters.

In foundation and several other applications, the soil is rarely in a dry condition.

Hence, Lovisa et al. (2010) conducted the direct shear tests to investigate the effects

of water content on the shear strength behaviour of a poorly graded sand (classified as

SP) reinforced with 0.25% randomly distributed glass fibres. The test results suggest

that the peak friction angle of the fibre-reinforced sand in moist condition is approx-

imately 3� less than that in dry condition for a relative density greater than 50%. At

the peak state, the fibre inclusions introduce an apparent cohesion intercept of 5.3 kPa

to the soil in the dry state, which remains almost unchanged by an increase in water

content. The ultimate-state shear strength parameters are independent of water

content and relative density. While the cohesion intercept of unreinforced sand at

ultimate state is zero, the inclusion of fibres causes an apparent cohesion of 2.6 kPa.

Falorca and Pinto (2011) studied the shear strength behaviour of poorly graded sand

(SP) and clayey soil of low plasticity (CL) reinforced with short, randomly distributed

PP fibres by conducting direct shear tests (60-mm square box). The test results show

that the fibres increase the shear strength and significantly modify shear stress-

displacement behaviour of the soil, as presented in Figs. 3.2 and 3.3. Shear strength

increases with increase in fibre content and fibre length. The increase in shear strength

Table 3.1 Direct shear test results of fly ash, silt and soil mixtures with fibre content (defined as

the ratio of weight of fibre solids to sum of weights of soil solids and fly ash solids), pf¼ 1%, for

the reinforced cases (After Kaniraj and Havanagi 2001)

Soil type

Unreinforced Fibre reinforced

c (kPa) ϕ (degrees) c (kPa) ϕ (degrees)

Fly ash 19.6 37.5 3.88 45.5

Silt 15.7 29.5 21.3 38.4

Mixture of 50% fly ash and 50% silt 14.7 36 32.5 35.1

Mixture of 50% of fly ash and 50% sand 9.8 33.0 17.4 39.4

Note: For fly ash reinforced with fibres ( pf¼ 0.5%), γdmax¼ 11.06 kN/m3 and wopt¼ 33.1%


0 0.05 0.10 0.15 0.20 0.25

90

110

130

150

170

190

210

230

250

a

b

Fibre content, fp (%)

Coh

esio

n (k

Pa)

Cement content,

cp = 8%

5%

0%

70

0 0.05 0.01 0.15 0.20 0.2527

29

31

33

35

37

39

41


Ang

le o

f in

tern

al f

rict

ion

(deg

rees

)

Cement content,

cp = 8%

5%

0%

Fig. 3.1 Variation of shear strength parameters with fibre content pf for uncemented and

cemented clayey soils after 28 days of curing: (a) cohesion c; (b) angle of internal friction ϕ(Adapted from Tang et al. 2007b)


Shear displacement, d (mm)

Shea

r st

ress

, t

(kPa)

0 2 4 6 8 10 120

50

100

150

200

250

300

350

a

b

Unreinforced sand

Fibre-reinforced sand

0.5% straight PP fibres 50 mm long fibres Effective normal stress = 219.39 kPa

0 2 4 6 8 10 1200

-0.5

0.5

1.0

Unreinforced sand

Fibre-reinforced sand

0.5% straight PP fibres 50 mm long fibresEffective normal stress = 219.39 kPa

Shear displacement, d (mm)Cha

nge

in v

olum

e, Δ

V (

kPa)

Fig. 3.2 Direct shear test results for fibre-reinforced sand: (a) shear stress τ versus shear

displacement δ; (b) change in volume of the specimen ΔV versus shear displacement δ (Adaptedfrom Falorca and Pinto 2011)


a

b

Fig. 3.3 Direct shear test results for fibre-reinforced clay: (a) shear stress τ versus shear displace-ment δ; (b) change in volume of the specimen ΔV versus shear displacement δ (Adapted from

Falorca and Pinto 2011)


is found to be more important for low normal stresses. No appreciable advantage is

achieved by using the crimped (texturized) fibres as far as the shear strength is

concerned. There is an increase in both apparent cohesion and the angle of shearing

resistance of soils due to inclusion of fibres. The initial stiffness of the reinforced

sand decreases with an increase in fibre content, whereas for reinforced clay, there is

no significant change.

Falorca and Pinto (2011) also studied how the fibres interact with soil particles

using both an optical microscope and a scanning electron microscope. Their study

shows that the fibres do not rupture during shear, but they are stretched, and

some damage may occur (Fig. 3.4). The damage is essentially fibre indentation,

with hardly any cutting. It is believed that the damage mostly occurs during

compaction as a result of high impact energy. The fibres lose their straightness

and end up with many bends (angularities). Michalowski and Zhao (1996) have

also suggested that the fibre kinking may occur during the deformation process.

Although the fibres suffer from some permanent localised damage, they are still

suitable for soil reinforcement, as the soil particles are held by the indentations in

the fibres. The contact area between soil particles and fibres pressed against each

other is proportional to the applied load until the fibres undergo plastic defor-

mation (i.e. surface imprints). These imprints allow adhesion to take place within

the reinforced soil mass. Note that the fibre prevents the soil particles from

packing tightly until fibre stretch and imprinting occur, thus increasing the

capacity to hold the particles and therefore allowing adhesion to develop. This

mechanism also explains why fibre-reinforced soils have a lower unit weight than

unreinforced soils.

Fibre

a

Soil particles

Fibre

Soil particles

b

Fig. 3.4 Interaction mechanisms between fibre and soil particles: (a) soil particles being

prevented by fibre from packing tightly; (b) soil particles causing fibre stretch and imprints on

the fibre, thus allowing adhesion to develop (Adapted from Falorca and Pinto 2011)


3.3.2 Observations in Triaxial Tests

Based on the triaxial compression tests, the improvement in shear strength of soil as

a result of inclusion of fibre reinforcement can be expressed in terms of the deviatorstress improvement factor Id, defined as

Id ¼ Δ σ1 � σ3ð Þσ1 � σ3ð ÞfU

¼ σ1 � σ3ð ÞR � σ1 � σ3ð ÞfUσ1 � σ3ð ÞfU

¼ σ1 � σ3ð ÞRσ1 � σ3ð ÞfU

� 1 ð3:3Þ

where (σ1� σ3)fU is the failure deviator stress of the unreinforced soil specimen,

and (σ1� σ3)R is the deviator stress of the fibre-reinforced soil specimen

corresponding to the axial strain ε(¼εfU) of the unreinforced soil specimen at

failure. The factor Id basically presents a relative gain in deviator stress of soil

specimen due to inclusion of fibres and is normally expressed as a percentage.

Note that in Eq. (3.3), (σ1� σ3)R can be the deviator stress of the reinforced soil

specimen at any selected/permissible axial strain as required for the safety of the

specific structure under consideration. For (σ1� σ3)R ¼ (σ1� σ3)fR at ε¼ εfR (axial

strain of reinforced soil specimen at failure), Eq. (3.3) reduces to the deviator stressimprovement factor at failure Idf, given as

Idf ¼ Δ σ1 � σ3ð Þfσ1 � σ3ð ÞfU

¼ σ1 � σ3ð ÞfR � σ1 � σ3ð ÞfUσ1 � σ3ð ÞfU

¼ σ1 � σ3ð ÞfRσ1 � σ3ð ÞfU

� 1 ð3:4Þ

The improvement in shear strength of soil as a result of inclusion of fibre

reinforcement can also be expressed in terms of deviator stress ratio (DSR) ordeviator stress ratio at failure (DSRf), as defined below:

DSR ¼ σ1 � σ3ð ÞRσ1 � σ3ð ÞfU

ð3:5Þ

DSRf ¼ σ1 � σ3ð ÞfRσ1 � σ3ð ÞfU

ð3:6Þ

The brittleness index, as defined below, is also used to describe the behaviour offibre-reinforced soil in triaxial compression (Maher and Ho 1993; Consoli et al.

1998a; Consoli et al. 2002):

Ib ¼σ1 � σ3ð Þpeak � σ1 � σ3ð Þultimate

σ1 � σ3ð Þultimate

¼ σ1 � σ3ð Þpeakσ1 � σ3ð Þultimate

� 1 ð3:7Þ

where (σ1� σ3)peak and (σ1� σ3)ultimate are peak and ultimate deviator stresses,

respectively. A lower value of Ib indicates that there is limited loss of post-peak

strength in the triaxial compression, and the fibre-reinforced soil behaves as a

ductile material.


The strain energy absorption capacity, which represents the ductility behaviour

of the material, is often defined as the area under the stress-strain curve up to 10%

strain. A higher strain energy absorption capacity indicates that the material is more

ductile.

The factors/ratios/indices as defined here have been used directly or indirectly by

the researchers to describe the effects of fibre inclusions on the soil characteristics.

Hoare (1979) presented the results of compaction and triaxial compression tests

on dry, angular crushed sandy gravel mixed with polymeric fibres and small strips

cut from a geotextile. The results show that the reinforcement offers resistance to

densification and has beneficial effects on both strength and ductility, except when

the increased amount of reinforcement results in reduced density, in which case the

strength may even decrease.

The triaxial compression investigation by Gray and Al-Refeai (1986) indicates

that the inclusion of natural and synthetic glass fibres in sand increases its strength

(expressed as the major principal stress at failure) and modifies the stress-

deformation behaviour with increased stiffness. The increase in strength with

fibre content varies linearly up to a fibre content of 2% by weight and thereafter

approaches an asymptotic upper limit. The rate of increase is roughly proportional

to the fibre aspect ratio. At the same aspect ratio, the confining pressure and the

weight fraction, roughness (not stiffness) of fibres tends to be more effective in

increasing the strength. Fibre-reinforced specimens fail along a classic planar shear

plane, whereas the sand reinforced with fabric (geotextile) layers fails by bulging

between the fabric layers. The existence of a critical confining pressure is common

to both the fibre-reinforced sand and the fabric-reinforced sand.

Maher (1988) performed laboratory triaxial compression tests on sand

reinforced with discrete, randomly distributed glass fibres. The results presented

by Maher (1988) and Maher and Gray (1990) indicate the following:

1. Sands reinforced with randomly distributed fibres exhibit either curved-linear or

bilinear principal stress envelopes. Uniform, rounded sand exhibits the former

behaviour (Fig. 3.5a), whereas the well-graded or angular sand tends to exhibit

the latter (Fig. 3.5b). The break in the bilinear curve or transition from a curved

to a linear envelope occurs at the threshold confining stress, which is referred to

as the critical confining stressσ3crit.2. Failure surfaces in a triaxial compression test on randomly distributed fibre-

reinforced sand are planar and oriented in the same manner as predicted by the

Mohr-Coulomb failure criterion, viz. at the angle of obliquity, or (45∘+ϕ/2),where ϕ is the angle of internal friction of sand. This finding suggests an

isotropic reinforcing action with no development of preferred planes of weak-

ness or strength.

3. An increase in fibre aspect ratio results in a lower σ3crit and higher fibre

contribution to shear strength. Fibres with very low modulus (e.g. rubber)

contribute little to increased strength in spite of superior pullout resistance

(low σ3crit).


4. Shear strength increases approximately linearly with increasing fibre content and

then approaches an asymptotic upper limit governed mainly by confining stress

and fibre aspect ratio (Fig. 3.6).

5. A better gradation or an increase in coefficient of uniformity of soil results in a

lower σ3crit and higher fibre contribution to strength, with all other factors being

constant.

a

b

Fig. 3.5 Principal stress envelopes from triaxial compression tests on reinforced sands: (a)

Muskegon dune sand; (b) mortar sand (Adapted from Maher and Gray 1990). (Note: Glass fibre

content ¼ 3%; 1 kg/cm2 ¼ 98.07 kPa)


6. An increase in soil particle size D50 has no effect on σ3crit. However, it reducesthe fibre contribution to strength, with all other factors being constant.

7. An increase in particle sphericity results in a higher σ3crit and lower fibre

contribution to strength, with all other factors being constant.

Al-Refeai (1991) conducted a series of triaxial tests to investigate the load-

deformation behaviour of fine and medium sands reinforced randomly with discrete

PP and glass fibres. The results show that shorter fibres (�25 mm) require a great

confining stress to prevent bond failure regardless of size and shape of sand

particles. Short fibres decrease the stiffness of medium sand. Soil-inclusion friction

interaction depends mainly on the extensibility of the inclusion rather than the

mechanical properties of sand. Fine sand with subrounded particles shows a more

favourable response to fibre reinforcement than medium sand with subangular

particles. The percentage increase in principal stress and secant modulus from the

inclusion of glass fibres is directly proportional to fibre length for a constant fibre

content. There is an optimum length (75 mm) of fibre for maximizing the strength

and stiffness of fibre-reinforced fine and medium sands.

Ranjan et al. (1994, 1996) carried out a series of triaxial compression tests to

study the stress-strain behaviour of plastic-fibre-reinforced poorly graded fine sand.

The inclusion of plastic fibres (aspect ratio ¼ 60–120, diameter ¼ 0.3–0.5 mm,

specific gravity ¼ 0.92, tensile strength ¼ 30 MPa, tensile modulus ¼ 2 GPa, skin

friction angle ¼ 21�) causes an increase in peak shear strength and reduction in the

loss of post-peak strength of sand. Figure 3.7 shows the stress-strain plot of the

Fig. 3.6 Effect of glass fibre content and aspect ratio on strength increase in Muskegon sand at

low and high confining stresses (Adapted from Maher and Gray 1990). (Note: 1 kg/cm2 ¼98.07 kPa)


reinforced soil. Thus, the residual strength of fibre-reinforced sand is higher as

compared to that of unreinforced sand. The principal stress envelopes for fibre-

reinforced sand are bilinear having a break at a confining stress, called the critical

confining stress, below which the fibres tend to slip or pullout. An increase in fibre

aspect ratio results in a lower critical confining stress and higher contribution to

shear strength, as also reported earlier by Maher and Gray (1990). Shear strength

increases approximately linearly with increasing fibre content up to 2% by weight,

beyond which the gain in strength is not appreciable.

Maher and Ho (1993) presented the effect of randomly distributed glass fibre

reinforcement on the response of cemented standard Ottawa sand under both static

and cyclic loads by conducting triaxial static and cyclic compression tests on

28-days cured specimens at a constant void ratio of 0.62. The test results, as

presented in Fig. 3.8, indicate that the addition of fibres significantly increases the

peak compressive strength of cemented sands. The study also shows the following:

1. The increase in peak compressive strength is more pronounced at higher fibre

contents.

2. The contribution of fibres to increased strength is more for longer fibre lengths

and lower confining stresses. Apparently at higher confining stresses, the soil is

Fig. 3.7 Stress-strain behaviour of plastic fibre-reinforced fine sand (Adapted from Ranjan et al.

1994, 1996)


already stiff and the cement or fibre’s contribution to strength is not effective as

observed under low confining stress.

3. The brittleness index increases with increasing fibre content and length, but

decreases with increasing confining stress.

4. The addition of fibres significantly increases the energy absorption capacity of

cement-stabilized sand. An increase in energy absorption is more pronounced at

higher fibre contents, longer fibre lengths and lower confining stresses.

5. In the triaxial compression test, no significant volume change takes place during

the cell pressure application, while during the shearing stage, a strong volume

expansion is observed under low confining pressure, which diminishes with

increasing confining pressure.

6. In comparison to cement-stabilized sand, where the addition of cement does not

affect the angle of internal friction and only increases the cohesion intercept

(Clough et al. 1981), the fibre inclusion increases both the angle of internal

friction and the cohesion intercept of cement-stabilized sand as the peak shear

strength parameters obtained in the tests indicate (see Table 3.2). Increasing the

fibre length (or aspect ratio) results in increased angle of internal friction angle

and cohesion intercept of cement-stabilized sand. The ultimate shear strength

parameters are relatively consistent. With the addition of 3% fibres to cemented

sand, the ultimate angle of internal friction angle increases from 32�to 39

�, and

ultimate cohesion intercept increases from 20 to 250 kPa.

Fig. 3.8 Effect of glass fibre inclusion on stress-strain behaviour of cement-stabilized standard

Ottawa sand after 28 days of curing (Adapted from Maher and Ho 1993)


7. The initial tangent modulus Ei for cement-stabilized fibre-reinforced sand

increases approximately linearly with increasing confining stress σ3 on log-log

scales when both are normalized to atmospheric pressure pa. Similar to cement-

stabilized sands (Clough et al. 1981), the following relationship holds good:

Ei ¼ kpaσ3pa

� �n

ð3:8Þ

where k is the intercept at σ3/pa¼ 1.0 and n is the slope of the line of variation ofEi/pa versus σ3/pa on log-log scale. As the fibre content increases from 0.5 to 3%,

the value of k increases from 700 to 1150, while the value of n decreases from

0.41 to 0.24, respectively.

8. The addition of fibres significantly increases the cyclic strength of cement-

stabilized sand. The number of cycles and the magnitude of strain required to

cause failure in cement-stabilized sand increases significantly as a result of fibre

inclusion.

Michalowski and Zhao (1996) conducted a series of triaxial tests on coarse,

poorly graded sand reinforced isotropically with galvanized or stainless steel

(specific gravity ¼ 7.85) and polyamide monofilament (specific gravity ¼ 1.28).

Compaction of the specimens was characterized by the void ratio as the relative

density is not an appropriate parameter for characterizing the fibre-reinforced

specimens, because the minimum and maximum void ratios of the reinforced soil

are very much dependent on the fibre characteristics. In all tests, the initial void

ratio of prepared specimens was 0.66, corresponding to a relative density of 70% of

unreinforced sand. They reported the stress-strain behaviour similar to that shown

in Fig. 3.7. The results show that the addition of steel fibres to sand leads to an

increase in the peak deviator/shear stress of about 20% ( pvf¼ 1.25%, ar¼ 40) for

specimens tested under a confining pressure of 100–600 kPa; this relative increase

is larger at a very low confining pressure (50 kPa). The specimens exhibit a typical

compaction effect at small axial strain and dilation at larger strains. The presence of

fibres inhibits the dilation effect to a certain degree. The increase in the content of

steel fibres leads to a clear increase in the peak deviator/shear stress and also leads

Table 3.2 Peak shear strength parameters (After Maher and Ho 1993)

Cement-stabilized sand without and with fibres

(admixture % by weight)

Angle of internal

friction (degrees)

Cohesion

intercept (kPa)

Sand + 4% cement 37 103

Sand + 4% cement + 0.5% fibres 41 104

Sand + 4% cement + 1% fibres 43 152




to an increase in the stiffness of the reinforced soil prior to reaching the failure. An

increase in the aspect ratio of the fibres contributes to a significant increase in the

peak deviator/shear stress. Inclusion of polyamide fibres leads to similar effects

with some deviation. Polyamide fibres produce a significant increase in the peak

deviator/shear stress for larger confining pressures, but the effect is associated with

a considerable loss of stiffness prior to failure and a substantial increase of strain to

failure. At a confining pressure of 100 kPa, however, no increase of the peak

deviator/shear with respect to the sand alone is recorded.

Kaniraj and Havanagi (2001) conducted unconsolidated undrained (UU) triaxial

compression tests on cylindrical specimens (diameter ¼ 37.7 mm, length ¼73.5 mm) of Rajghat fly ash, Delhi silt, mixture of 50% Rajghat fly ash and 50%

Delhi silt and mixture of 50% Rajghat fly ash and 50% Yamuna sand with and

without random distribution of PET fibre reinforcement, compacted at respective

maximum dry unit weight-optimum water content states. Confining stresses in the

range of 24.5–392.3 kPa were used. The tests results suggest the following:

1. In unreinforced specimens, the deviator strain attains a peak and thereafter

remains constant. The strain to attain the peak deviator stress increases with an

increase in confining stress.

2. In fibre-reinforced specimens, no peak deviator stress is reached even at 15%

axial strain. This may be a manifestation of the ductile behaviour induced by the

fibre inclusions.

3. Table 3.3 provides the values of total stress-strength parameters cuu and ϕuu. The

data in this table show that there is a significant increase in both cuu and ϕuu due

to fibre inclusions.

4. The failure envelope plotted as the variation of the major principal stress at

failure (15% axial strain) σ1f with confining stress σ3 is bilinear for the fibre-

reinforced fly ash-soil specimens. The initial steeper portion is characterized by

the pullout failure of the fibres and the second linear portion by the rupture of the

fibres, as reported by Maher and Gray (1990).

5. The value of Idf increases as (σ1� σ3)fU increases, as per the following

correlation:

Table 3.3 Shear strength parameters, based on UU triaxial compression tests, of fly ash and soil

mixtures with fibre content (defined as the ratio of weight of fibre solids to sum of weights of soil

solids and fly ash solids), pf¼ 1%, for the reinforced cases (After Kaniraj and Havanagi 2001)

Soil type


cuu (kPa) ϕuu (degrees) cuu (kPa) ϕuu (degrees)

Fly ash 43.2a 30.2a 128.6a 36.1a

Mixture of 50% fly ash and 50% silt 25.8 30.2 93.3b 40.0b

Mixture of 50% of fly ash and 50% sand 16.5 30.4 160.0b 32.9b

aFor σ3> 50 kPabFor σ3> 25 kPa


Idf ¼ 16809 σ1 � σ3ð ÞfU� ��0:8059 ð3:9Þ

The standard error in logIdf and the coefficient of determination R2 of the

correlation are 0.073 and 0.885, respectively.

6. Even though the fibre inclusions increase the deviator stress at large strain, they

do not necessarily increase the stiffness at small strain. The values of secant

modulus Es calculated at (σ1� σ3)fR/2 and (σ1� σ3)fU/2 show that the fibre

inclusions decrease Es of fly ash-soil specimens, but this trend is not consistent

at all confining stresses in pure fly ash.

Consoli et al. (2002) carried out the drained triaxial compression tests on a

uniform fine sand (SP) reinforced with PET fibres, with and without rapid-

hardening Portland cement. The results show that with the inclusion of fibres and

increase in fibre length, the cohesive intercept of sand does not change, whereas the

friction angle increases. The fibre reinforcement does not affect the initial stiffness

or ductility of the uncemented sand. As expected, the addition of cement to the sand

significantly increases the stiffness and peak strength and changes the soil behav-

iour from ductile to a noticeable brittle one. The cement content increases both the

peak friction angle and the cohesive intercept. The initial stiffness of the cemented

sand is not affected by fibre inclusion, because it is basically a function of cemen-

tation. The efficiency of the fibre reinforcement when applied to cemented sand is

found to be dependent on the fibre length. The greatest improvements in triaxial

strength, ductility and energy absorption capacity (defined as the amount of energy

required to induce deformation and is equal to area below stress-strain curve) are

observed for the longer (e.g. 36 mm) fibres.

Babu et al. (2008a) carried out standard triaxial compression tests on coir fibre-

reinforced sand for several fibre contents (0, 0.5, 1 and 1.5% by dry weight of sand).

The total unit weight of soil specimens in all tests was kept at a constant value of

14.8 kN/m3. The results as presented in Fig. 3.9 show that the stress-strain response

of soil is improved considerably by the addition of coir fibres.

Babu and Vasudevan (2008a) also reported the following characteristics of coir

fibre-reinforced soil based on the standard triaxial compression test results:

1. The deviator stress at failure can increase up to 3.5 times over unreinforced/plain

soil by fibre inclusion.

2. Maximum increase of stress is observed when the fibre length is between 15 and

25 mm, that is, when the length is 40–60% of the least lateral dimension of the

triaxial test specimen.

3. Stiffness of soil increases considerably due to fibre inclusion; hence immediate

settlement of soil can be reduced by incorporating fibres in the soil.

4. Energy absorption capacity of fibre-reinforced soil increases as the fibre content

increases, and hence toughness of soil can be increased with fibre inclusion.


Babu et al. (2008b) examined the use of coir fibres as reinforcement to improve

the engineering properties of black cotton soil (expansive soil) by conducting

standard undrained triaxial compression tests. The deviator stress at failure

increases with increase in the fibre content as well as with increase in the diameter

of the fibres. The maximum increase of major principal stress at failure is found to

be 1.30 times over the unreinforced soil. The coir fibres help reduce the swell

potential of black cotton soil.

Kumar and Singh (2008) conducted triaxial compression tests to study the

behaviour of fly ash reinforced with PP fibres. The results, as presented in

Table 3.4, show that the deviator stress at failure increases with an increase in

fibre content at a particular cell pressure; but the increments are more significant up

to 0.3% fibre content, and the gain in deviator stress is reduced for high fibre

contents. The deviator stress also increases with an increase in aspect ratio, but the

gain in deviator stress is lower for the aspect ratio more than 100. Based on the

cyclic triaxial tests, it is observed that the resilient modulus of fly ash increases due

to inclusion of fibres in fly ash.

In triaxial compression, a considerable increase of shear strength is contributed

by the presence of fibres, while in extension, the benefit of fibres is very limited.

This behaviour confirms that the tamping technique in the moist condition gener-

ates preferential near-horizontal orientation of fibres, that is, the anisotropic distri-

bution of fibre orientation (Diambra et al. 2010).

The PP crimped fibres in loose sandy soil reduce the potential for the occurrence

of liquefaction in both compression and extension triaxial loadings and convert a

Fig. 3.9 Stress versus strain curves for coir fibre-reinforced sand (Adapted from Babu et al.

2008a)


strain-softening response into a strain-hardening response. When the full liquefac-

tion of reinforced specimens is induced by strain reversal, the lateral spreading of

soil seems to be prevented (Ibraim et al. 2010).

Hamidi and Hooresfand (2013) conducted conventional triaxial compression

tests to determine the effect of cement and PP fibres on the strength behaviour of

clean and uniform beach sand. The test results show that addition of PP fibres to the

cemented soil causes the following:

1. Increase in peak and residual shear strengths as a result of increase in angle of

internal friction angle and cohesion intercept. The effect of fibre content on shear

strength is greater at higher relative densities of sand.

2. Decrease in initial stiffness and brittleness indexIb.3. Increase in energy absorption capacity. This indicates that the fibres change the

brittle behaviour to ductile behaviour; the change is more for greater relative

density under higher confinement.

Mixing of synthetic fibres (PP fibres and geogrid waste fibres) increases the

strength of rice husk ash (RHA), but there exists an optimum fibre content of 1.25%

at which the reinforcement benefits are maximum. The stress-strain behaviour of

RHA improves considerably due to an increase in fibre content. The secant modulus

of reinforced RHA increases with an increase in fibre content up to 1.25%, and

thereafter it decreases. The shear strength parameters (cohesion intercept and angle

of internal friction) also increase with an increase in fibre content up to 1.25%, and

thereafter they decrease (Jha et al. 2015).

Example 3.1

Consider the following values of the deviator stress at failure:

For unreinforced soil, (σ1� σ3)fU¼ 162 kPa

For fibre-reinforced soil, (σ1� σ3)fR¼ 338 kPa

Table 3.4 Variation of deviator stress at failure with aspect ratio, cell pressure and fibre content

for fibre-reinforced fly ash (After Kumar and Singh 2008)

Fibre aspect ratio Cell pressure (kPa)

Deviator stress (kPa) at failure with fibre content (%)

0.0 0.1 0.2 0.3 0.4 0.5

80 40 162 212 262 300 320 338

70 184 267 334 382 405 422

100 210 92 362 426 453 471

140 242 320 405 462 498 543

100 40 162 259 320 368 386 398

70 184 287 359 405 426 450

100 210 315 392 443 469 487

140 242 332 424 486 520 563

120 40 162 262 322 367 393 407

70 184 294 368 409 438 456

100 210 320 398 451 476 493

140 242 338 427 490 527 568


Determine the deviator stress improvement factor at failure. What does this

indicate?

Solution

From Eq. (3.4), the deviator stress improvement factor is

Idf ¼ σ1 � σ3ð ÞfRσ1 � σ3ð ÞfU

� 1 ¼ 338

162� 1 � 1:09 or 109%

This value of Idf shows that inclusion of fibres into the soil causes 109% increase

in the deviator stress at failure.

3.4 Unconfined Compressive Strength

The improvement in unconfined compressive strength (UCS) of soil as a result of

inclusion of fibre reinforcement can be expressed in terms of the unconfinedcompressive strength improvement factor IUCS, defined as

IUCS ¼ qUR � qUUqUU

¼ qURqUU

� 1 ð3:10Þ

where qUR is the UCS of fibre-reinforced soil and qUU is the UCS of unreinforced

soil. Basically, the factor IUCS presents the relative gain in UCS of soil due to

inclusion of fibres and is normally expressed as a percentage. Note that IUCS¼ Idffor σ3¼ 0 in Eq. (3.4).

Note that the unconfined compressive strength improvement factor can be

defined for the same selected/permissible axial strains for reinforced and

unreinforced soils as the shear strength improvement factors have been defined

earlier. Hence, the unconfined compressive strength improvement factor can also be

expressed as:

IUCS ¼ qR � qUUqUU

¼ qRqUU

� 1 ð3:11Þ

where qR is the unconfined compressive stress on the fibre-reinforced soil specimen

corresponding to the axial strain ε(¼εfU) of the unreinforced soil specimen at

failure. The factor IUCS basically presents the relative gain in shear strength of

soil due to inclusion of fibres and is normally expressed as a percentage.

Freitag (1986) investigated the influence of synthetic fibre inclusions (diameter

¼ 0.1–0.2 mm, length¼ 20 mm) on the UCS of a compacted fine-grained soil (lean

sandy clay, CL). The test specimens for the unconfined compression tests were

compacted over a sufficiently wide range of water content to define the compaction

curve. The soil was mixed with water, and then the desired amount of fibres was

3.4 Unconfined Compressive Strength 65

added and mixed into the soil. Fibre content was 1% by volume. The unconfined

compression tests were performed immediately after compaction. The compacted

soil layers were thin relative to the length of the fibres, so in the final compacted

state, the fibres were not truly randomly oriented in the specimens. The results

indicate the following:

1. UCS of the reinforced soil compacted near and wet of optimum is greater than

for unreinforced soil at the same water content. For specimens compacted well

on the dry side of optimum, there does not seem to be any benefit from the

presence of the fibres.

2. The type of fibre used does not seem to have a significant effect on strength.

3. The maximum UCS occurs somewhat dry of optimum and is not greatly differ-

ent for unreinforced and reinforced soils.

4. At higher water contents, the strength of the unreinforced soil decreases more

rapidly than that of the reinforced soil. An examination of the stress-strain curves

(Fig. 3.10) for specimens at the same water content shows that usually the

reinforced soil fails at a greater strain than the unreinforced soil. This is most

often the case for wet-side soil.

5. The stress-strain relations (Fig. 3.10) are similar at very low strains, but the

reinforced soil is able to hold together for more deformation and therefore higher

stress at rupture. Thus, the reinforced soil is also able to absorb more energy and

hence is ductile.

The laboratory investigation carried out by Santoni et al. (2001) indicates that an

inclusion of randomly oriented discrete PP fibres (synthetic monofilament, fibril-

lated, tape and mesh fibres) significantly improves the UCS of sands. An optimum

fibre length of 51 mm (2 in.) was identified for the reinforcement of sand specimens.

A maximum performance is achieved at the fibre content between 0.6 and 1% by

dry weight. The specimen performance is enhanced in both wet and dry of optimum

conditions. The inclusion of up to 8% of silt does not affect the performance of the

fibre reinforcement.

Axial strain, e (%)

Axi

alst

ress

, s(k

Pa)

Fibre-reinforced soil

Unreinforced soil

Fig. 3.10 Typical

unconfined compression

stress-strain curves for

unreinforced and fibre-

reinforced soils (Adapted

from Freitag 1986).


Kaniraj and Havanagi (2001) conducted unconfined compression tests on cylin-

drical specimens (diameter¼ 37.7 mm, length¼ 73.5 mm) of Rajghat fly ash, Delhi

silt, mixture of 50% Rajghat fly ash and 50% Delhi silt and mixture of 50% Rajghat

fly ash and 50% Yamuna sand with and without random distribution of PET fibre

reinforcement, compacted at respective maximum dry unit weight-optimum water

content states. The axial stress-axial strain behaviour was markedly affected by the

fibre inclusions. In unreinforced specimens, a distinct failure stress was reached at

an axial strain of about 2%, whereas the fibre-reinforced soil specimens exhibited

more ductile behaviour, and no distinct reduction in axial stress was evident even at

15% axial strain. Table 3.5 presents the UCS of reinforced and unreinforced

specimens. You may notice that the unreinforced fly ash has a higher UCS than

silt and fly ash-soil mixtures. However, the inclusion of fibres improves the strength

of silt and fly ash-soil mixtures so much that their UCS even surpasses that of the

fibre-reinforced fly ash. The results in Table 3.5 show that IUCS decreases as qUUincreases. They developed the following correlation between IUCS and qUU with

standard error in logIUCS and coefficient of deamination R2 of the correlation to be

0.126 and 0.989, respectively:

IUCS ¼ 9038:3e�0:0619qUU ð3:12Þ

Equation (3.2) is applicable for specific soils and fibre content as used in the

experimental investigation by Kaniraj and Havanagi (2001).

Kaniraj and Havanagi (2001) also studied the effect of addition of 3% cement on

the unconfined strength behaviour of fly ash-silty soil mixtures reinforced with 1%

fibre. The results show that the UCS of a fly ash-soil mixture increases due to

addition of cement and fibres. Depending on the type of mixture and curing period,

the increase in UCS caused by the combined action of cement and fibres is either

more than or nearly equal to the sum of the increases caused by them individually.

For an intermediate cement content of 5%, an increase in fibre content from

0.1 to 0.9% causes average increases in UCS of sand by about 40%. The initial

stiffness of the cemented sand was not affected by fibre inclusion, since it is

basically a function of cementation. The positive effect of fibre length is generally

not detected in the unconfined compression tests, clearly indicating the major

influence of confining pressure and the necessity of carrying out triaxial compres-

sion tests to fully observe the fibre-reinforced soil behaviour (Consoli et al. 2002).

Table 3.5 Average UCS of fly ash, silt and soil mixtures with fibre content (defined as the ratio of

weight of fibre solids to sum of weights of soil solids and fly ash solids), pf¼ 1%, for the reinforced

cases (After Kaniraj and Havanagi 2001)

Soil type qUU(kPa) qUR(kPa) IUCS(%) (Eq. (3.10))

Fly ash 65.7 157.9 140

Silt 36.3 411.9 1035

Mixture of 50% fly ash and 50% silt 47.1 304.0 545

Mixture of 50% of fly ash and 50% sand 33.3 436.4 1211

Note: UCS values for fibre-reinforced specimens are the values of axial stress at 15% axial strain.


Tang et al. (2007b) conducted a series of unconfined compression test on clayey

soil cylindrical specimens (diameter¼ 39.1 mm, length¼ 80 mm) with inclusion of

different contents of PP fibres (12 mm long) and ordinary Portland cement. All the

test specimens were compacted at their respective maximum dry unit weight and

optimum water content. The specimens treated with cement were wrapped with

plastic membrane in the curing box for 7, 14 and 28 days, and they were submerged

under water for 24 h at the last day of each curing period. Figures 3.11a, 3.11b and

3.11c show the stress-strain curves for fibre-reinforced uncemented soil, cemented

soil and fibre-reinforced cemented soil with 5% cement after 28 days of curing.

Note that in Fig. 3.11, the axial stress is basically the unconfined compressive stress.

The peak/maximum value of axial stress is the UCS. The following are worth

mentioning:

1. Fibre inclusion with 0.05% fibre content enhances the unconfined compressive/

peak strength of uncemented soil, but the contribution of further increase of fibre

content to unconfined compressive strength decreases significantly (Fig. 3.11a).

0 1.0 2.0 3.0 4.0 5.00.5 1.5 2.5 3.5 4.5 5.5

50

100

150

200

250

300

a b

c

Axi

alst

ress

, σ(k

Pa)

Fibre content,

fp = 0.25%

0.15%

0.05%

0%

0

0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.00

100

200

300

400

500

600

700

Axi

alst

ress

, σ(k

Pa)

Cement content,

cp = 8%

5%

0%

0 1 2 3 4 5 6 70

200

400

600

800

1000

1200

Axial strain, ε (%)

Axial strain, ε (%) Axial strain, ε (%)

Axi

alst

ress

, σ(k

Pa)

fp = 0.25%

cp = 5%

0.15%

0.05%

Fig. 3.11 Stress-strain curves obtained from unconfined compression tests: (a) fibre-reinforced

uncemented clayey soil; (b) cement-stabilized clayey soil after 28 days of curing; (c) fibre-

reinforced cemented clayey soil with cement content pc¼ 5% after 28 days of curing (Adapted

from Tang et al. 2007b)


2. The fibre-reinforced uncemented soil exhibits more ductile behaviour and

smaller loss of post-peak strength than uncemented soil. The reduction in loss

of post-peak strength is more pronounced for higher fibre content (Fig. 3.11a).

3. The initial stiffness of uncemented soil is not affected significantly by the

addition of fibres (Fig. 3.11a).

4. The unconfined compressive strength increases dramatically with an increase in

cement content, and the cemented soil exhibits a marked stiffness and brittle-

ness, resulting in a sudden drop of post-peak strength to zero. Its failure strain is

0.5–0.75% (Fig. 3.11b), which is much smaller than that of uncemented soil and

fibre-reinforced cemented soil.

5. The inclusion of fibres within the cemented soil reduces the brittleness with a

gradual reduction of post-peak strength. The failure strain increases and ranges

from 1.25 to 1.7% (Fig. 3.11c).

Note that the failure mechanism of cemented soil is triggered by the formation of

noticeable wide and long tension cracks. With the presence of fibres in cemented

soil, the tension cracks become gradually narrower and shorter with increasing fibre

content (Fig. 3.12). In fact, the fibres added to cemented soil serve as bridges and

impede the opening and development of cracks, thereby changing the brittle

behaviour to ductile behaviour.

Kumar and Singh (2008) reported the improvement in unconfined compressive

strength of fly ash with random inclusion of PP fibres. At an aspect ratio of 100, the

unconfined compressive strength of fly ash increased from 128 to 259 kPa with

increment in fibre content from 0 to 0.5%. The results show that the variation of

unconfined compressive strength with fibre content is linear, while with aspect

ratio, the variation is nonlinear. The optimum fibre length and aspect ratio were

found as 30 mm and 100, respectively.

Park (2009) examined the effect of fibre concentration and distribution on the

UCS of fibre-reinforced cemented sand. A series of unconfined compression tests

were performed on artificially cemented sand specimens with layered polyvinyl

alcohol (PVA) fibre reinforcement. The fibres were randomly reinforced at a

predetermined layer among five compacted layers in the cylindrical soil specimens

Fig. 3.12 Effect of fibres on the failure pattern of cement-stabilized clayey soil in unconfined

compression tests with cement content, pc¼ 8%: (a) fibre content, pf¼ 0%; (b) pf¼ 0.05%; (c)

pf¼ 0.25% (After Tang et al. 2007b)


(length ¼ 140 mm; diameter ¼ 70 mm). The results show that the UCS of the

reinforced soil increases gradually as the number of fibre inclusion layers increases.

A fibre-reinforced specimen, where fibres were evenly distributed throughout the

five layers, was twice as strong as an unreinforced cemented specimen. Using the

same fibre content of 1% (as per Eq. (2.6)) to reinforce two different specimens, a

specimen with five fibre inclusion layers was 1.5 times stronger than a specimen

with one fibre inclusion layer at the middle of the specimen. Note that the cement

content as per Eq. (2.9) was 4% in the study.

Zaimoglu and Yetimoglu (2012) investigated the effects of randomly distributed

PP fibre reinforcement (length ¼ 12 mm; diameter ¼ 0.05 mm) on the UCS of a

fine-grained soil (MH, high plasticity soil) by conducting a series of unconfined

compression tests. The test results show that the UCS of soil tends to increase with

increasing fibre content as shown in Fig. 3.13. However, the rate of increase in UCSis not significant for a fibre content greater than 0.75%. Compared to the

unreinforced soil specimen, the UCS of the reinforced soil specimen at 0.75%

fibre content increases by approximately 85% (i.e. from 392 to 727 kPa). The

increase in UCS might be due to the bridging effect of fibre which can efficiently

impede the further development of failure planes and deformations of the soil, as

Tang et al. (2007b) also discussed in their study. The shape of the soil specimens

after the tests indicates the bulging failure mode along with presence of the bridging

effect of fibres (Fig. 3.14).

Mirzababaei et al. (2013) studied the effect of inclusion of carpet waste fibres on

the UCS of clay soils. The test results suggest the following:

1. The UCS of fibre-reinforced clay soil is highly dependent on dry unit weight,

water content and fibre content. At a constant dry unit weight and water content,

an increase in the fibre content results in a significant increase in the UCS value.However, unreinforced and fibre-reinforced clay soil specimens prepared at their

0 0.25 0.5 0.75 10

200

600

400

800

1000


UC

S (k

Pa)

Fig. 3.13 Effect of fibre content on unconfined compressive strength of fine-grained soil (Adapted

from Zaimoglu and Yetimoglu 2012)


respective maximum dry unit weight and optimum water content show a reduc-

tion in the UCS value with an increase in fibre content.

2. An increase in the dry unit weight of reinforced clay specimens prepared at a

constant water content and fibre content results in a significant increase in UCS.3. An increase in water content of reinforced specimens at the same dry unit weight

and fibre content results in a reduction in the UCS.4. A combined increase in dry unit weight and water content at a constant fibre

content results in an increase in the UCS.5. Unreinforced soil specimens show the brittle behaviour and fail at a very small

axial strain (less than 1%), whereas reinforced specimens at 5% fibre content fail

at a relatively large axial strain (15% or more) with strain hardening and ductile

behaviour.

6. Failure patterns of unreinforced soil specimens are evident as nearly vertical

shear planes. With an increase in fibre content, particularly at 5% fibre content,

the failure pattern is gradually transformed to plastic bulging with networks of

tiny cracks without an apparent shear failure plane.

The following points regarding the strength aspects of fibre-reinforced soils are

worth mentioning:

1. The unconfined compression test data indicate that 19.05 mm (0.75 in. might be

a minimum length of PP fibres to achieve some form of strength enhancement

of sandy soil. In general, increases in UCS on the order of 2–2.5 times that of

unreinforced soil can be realized at a PP fibre content of 0.1%. Comparable

strength increases are not gained for the glass fibre-reinforced soil until the

fibre content of 0.7% is realized. This high fibre content is difficult to handle in

the laboratory preparation of specimens, and this fibre content may be equally

unworkable in the field. No consistent trends are observed regarding vertical

strain moduli in the unconfined compression test. The modulus value varies

from positive to reduction. Fibres significantly increase the modulus of tough-

ness as determined from the unconfined compression test, serving as an indi-

cator of how fibres influence the ductility of the soil (Hoover et al. 1982).

Fig. 3.14 Fibre-reinforced fine-grained soil specimen after unconfined compression test – bulging

failure with bridging effect of fibres (After Zaimoglu and Yetimodlu 2012)


2. When tested in saturated condition in cyclic triaxial compression tests, in

comparison to sand reinforced with PP fabric, fine steel wire mesh and nylon

netting, the sand reinforced with randomly distributed fine PP fibres exhibits a

relatively higher increase in resistance to liquefaction (Uzdavines 1987;

Noorany and Uzdavines 1989).

3. The mechanism of failure of cylindrical soil specimens in unconfined com-

pression tests may differ from that in triaxial compression tests. The fibres are

likely to get pulled out in the unconfined compression tests, whereas in the

triaxial compression tests, they may tend to attain their tensile yield stress at

higher confining stresses as suggested by Maher and Gray (1990). Probably due

to this difference in failure mechanisms, the values of Idf in triaxial compres-

sion tests are not as high as the values of IUCS in unconfined compression tests

(Kaniraj and Havanagi 2001).

4. The addition of fibres causes the soil behaviour to diverge from the frictional

characteristics, so that the shear strength is no longer related to the volume

change. The effect of fibre inclusion on dilation and volume change is pro-

nounced at higher load and strain levels, probably due to the inhibiting action of

the fibres (Maher and Gray 1990; Heineck et al. 2005).

5. Inclusion of fibres increases the peak UCS and ductility of kaolinite clay, with

the increase being more pronounced at lower water contents of the fibre-

reinforced clay. Increase in fibre length reduces the contribution of fibres to

peak UCS, while increasing the contribution to energy absorption or ductility

(Maher and Ho 1994).

6. In the direct shear tests, the shear strength of dry sand reinforced with shredded

waste tyre fibres (length ¼ 6–150 mm) is affected significantly by normal

stress, fibre content and unit weight of sand. Adding tyre fibres increases the

shear strength of dry sand with an apparent friction angle as large as 67�. Onlythe shredded tyre fibres have friction angle of 30

�, while the friction angle of

sand varies from 25�to 34

�for loose condition (unit weight ¼ 15.5 kN/m3) and

dense condition (unit weight ¼ 17.7 kN/m3), respectively (Foose et al. 1996).

7. The triaxial compression test data reported by Consoli et al. (1998a) show that

the glass fibre reinforcement inclusion in cemented silty sand (SM) increases

both peak and residual strengths, decreases stiffness and changes the brittle

behaviour to more ductile as indicated by a significant reduction in the brittle-

ness index Ib. The peak strength increase is more effective for uncemented soil,

whereas the increase in residual strength is more effective when fibres are

added to soil containing cement. The peak friction angle of uncemented silty

sand increases from 35� to 46� due to inclusion of glass fibres, while the peak

cohesion intercept is just slightly affected by glass fibre inclusion, being a

function basically of cementation.

8. The test results of drained triaxial compression tests conducted by Michalowski

and Cermak (2002) indicate that the contribution of the monofilament polyam-

ide and galvanized steel fibres to the strength of sand is the largest when they

are placed in the direction of largest extension of the fibre-reinforced soil

(horizontal in the test). Vertical fibres in triaxial testing are subjected to


compression, and they have an adverse effect on the initial stiffness of the

reinforced soil and do not contribute to the strength. Specimens with a random

distribution of fibres exhibit a smaller increase in strength than those with

horizontal fibres, because a portion of randomly distributed fibres is subjected

to compression.

9. The engineering characteristics of fly ash and PET fibre-reinforced fly ash are

similar in drained and undrained triaxial compression tests. The deviator stress-

axial strain curves in the unconsolidated undrained and drained tests are

amenable for hyperbolic analysis (Kaniraj and Gayathri 2003).

10. The triaxial compression test data obtained by Consoli et al. (2003a) show that

the friction angle of low plasticity silty clayey sand is barely affected by

inclusion of PP fibres as its value increases from 30� to 31�, while the cohesionintercept increases from 23 to 127 kPa. The fibre-reinforced triaxial soil

specimens are observed to fail as a uniform bulging.

11. The results obtained from the unconfined compression tests and the triaxial

compression tests on fibre-reinforced soils should be used carefully in analysis

and design of fibre-reinforced soil structures as these tests have some limita-

tions. A general limitation is the length L of fibres with respect to size (diameter

d ) of the test specimen. The researchers have used different values of d/L ratios

varying from 0.17 to 10.2 in their studies. Ang and Loehr (2003) performed a

series of laboratory unconfined compression tests on specimens of a compacted

silty clay to evaluate how the size of specimens used for strength testing of

fibre-reinforced soil affects the measured strength and stress-strain properties.

Their study indicates that there is a significant effect of specimen size both in

terms of the magnitude of the measured strengths as well as in terms of the

variability of the measured strengths. The effects of specimen size are found to

be most important for specimens compacted at water contents dry of optimum

water content. For fibre lengths of less than 50 mm, probably use of specimens

with diameters of 70 mm or greater (i.e. d/L> 1.4) will produce strengths that

are reasonably representative of the true mass strengths of fibre-reinforced

soils.

12. The inclusion of stiff fibres, such as glass fibres (also, PET fibres), increases the

peak friction angle of both cemented and uncemented sand, as well as slightly

reduces the peak cohesive intercept and the brittleness of the cemented sand.

Relatively extensible fibres, such as PP fibres, exert a more pronounced effect

on the mode of failure (from brittle to ductile) and on the ultimate behaviour of

cemented sand. An increase in ultimate deviator stress is observed to be directly

proportional to the fibre length. Inclusion of glass fibres does not affect the

ultimate strength of the reinforced soil. The initial stiffness for both cemented

and uncemented soils is slightly affected by inclusion of PET and glass fibres,

but it dramatically decreases by inclusion of PP fibres, probably as a result of

loss of continuity of the cementitious links caused by the introduction of

relatively extensible fibres, which will work just under high deformations.

The increase in energy absorption capacity of soil is more if longer fibres are

included (Consoli et al. 2004).


13. Based on the direct shear tests, the cohesion intercept of black cotton soil

increases, and the angle of internal friction decreases with addition of 2% of

glass fibres. However, on further increasing fibre content, the cohesion

decreases, and the angle of internal friction increases (Gosavi et al. 2004).

14. The direct shear test results show that as the PP fibre content in poorly graded

sand increases, the percentage increase in peak shear stress increases up to

0.2% fibre content. Beyond 0.2% fibre content, the rate of percentage increase

in the peak shear stress decreases. As the normal stress increases, the increase

in peak shear stress of fibre-reinforced sand decreases. The angle of internal

friction of the fibre-reinforced sand is more than that of the unreinforced sand,

but an increase in the fibre content does not have a significant effect on the

angle of internal friction angle of sand. The increase in the length of the fibre

also does not affect the angle of internal friction. At 70% relative density, the

angles of internal friction of unreinforced and reinforced sands are comparable.

The percentage increase in strength of reinforced sand is more at 50% relative

density compared to 70% relative density. At higher relative density (70%), the

increase in fibre content does not have much effect on the strength of fibre-

reinforced sand (Gupta et al. 2006).

15. Rubber fibres (length ¼ 4–10 mm; diameter ¼ 0.3–1.5 mm) constitute discon-

tinuities in the soil phase. This can have a negative influence on the

compactability and strength of the reinforced clay. In general, the presence of

rubber fibres does not cause significant change in the drained and undrained

strength of the clay (Ozkul and Baykal 2006).

16. Latha and Murthy (2007) investigated the effects of reinforcement form on the

mechanical behaviour of a dry river sand (SP) at 70% relative density by

conducting a series of triaxial compression tests on unreinforced and reinforced

sand with three different reinforcement forms, namely, planar/horizontal rein-

forcements (PP geotextile and PET geogrid) of circular shape (diameter ¼38 mm), discrete strip PET fibres (length ¼ 11 mm; width ¼ 2 mm) and

cylindrical geocells made from geotextile or geogrid by stitching with PET

threads. The test results indicate that the discrete fibre form of reinforcement is

inferior compared to the planar or cellular forms. This may be because of

reduction in overall confinement effect due to small-size fibre elements.

Among the three forms of reinforcement, the geocell is the most effective in

improving the strength. The stress-strain curves for geocells at all confining

pressures are found to be almost flat after peak is reached unlike in case of other

two forms where the post-peak strength loss is observed. PET geocells are

highly efficient in improving the strength of sand compared to PP geotextile

cells.

17. Use of coir and PP fibres increases theUCS value of silty sand and silty sand-flyash mixes. The optimum amount of fibres is found to be 0.75% of coir fibres

and 1% of PP fibres. The resilient strain is less in soil reinforced with coir fibres

than with PP fibres, indicating that coir fibres can help in delaying the failure of

subgrade in pavement systems. This is probably due to higher interface friction

angle of coir fibres with soil (Chauhan et al. 2008).


18. The unconfined compressive strength reaches its maximum value at a PP fibre

(7 mm long)/fat clay (CH) ratio of 1.0% and poorly graded sand (SP)/fat clay

(CH) ratio of 7.5%. There is a reasonably strong linear correlation (R2� 1.0)

between UCS and average initial tangent modulus values. As the sand content

increases from 5 to 10%, the average initial tangent modulus increases and

reaches its maximum value at 7.5% sand content (Yilmaz 2009).

19. The direct shear test results show that the shear strength improvement of sand

induced by inclusion of tyre buffings (length¼ 8–50 mm; thickness¼ 2–5 mm)

is sensitive to the amount of applied normal stress. The shear strength of sand

increases with increasing content of tyre buffings up to a maximum value for

buffings content in the vicinity of 20%. Internal friction angle of sand increases

from 34� to as large as 45�. Increasing the aspect ratio of tyre buffings from 2 to

12.5 leads to an increase of the overall shear strength of sand. This is probably

due to an increased contact area with the soil particles (Edincliler and Ayhan

2010).

20. The direct shear tests conducted by Zaimoglu and Yetimoglu (2012) on ran-

domly distributed PP fibre-reinforced fine-grained soil (MH, high plasticity

soil) show that the value of cohesion intercept of soil increases with increasing

fibre content up to a value of around 0.75%. However, the angle of shearing

resistance does not change significantly with fibre content. These observations

might be attributed to the fact that the randomly distributed fibres act as a

spatial three-dimensional network to interlock soil particles to form a unitary

coherent matrix and restrict any displacements, thus resulting in increased

cohesion, but the individual fibre inclusions might not have discernible effect

on the microstructure of soil, thus not affecting the angle of shearing resistance

of soil (Tang et al. 2007b; Zaimoglu and Yetimoglu 2012).

21. The silica fume (a waste product obtained as a by-product of producing silicon

metal or ferrosilicon alloys), scrap tyre rubber fibres (length ranging from 5 to

10 mm; thickness ranging from 0.25 to 0.5 mm; width ranging from 0.25 to

1.25 mm) and silica fume-scrap tyre rubber fibre mixtures increase the UCS of

clayey soil. The maximum value of UCS is obtained by addition of 20% silica

fume and 2% fibre. The direct shear test results indicate that the maximum

cohesion and internal friction angle values are also obtained by addition of 20%

silica fume and 2% fibre (Kalkan 2013).

22. The cyclic triaxial compression test results show that the presence of monofil-

ament PP fibres (length ranging from 6 to 18 mm) has a significant effect in

reducing the liquefaction susceptibility of poorly graded beach sand (classified

as SP).The number of load cycles causing liquefaction increases with an

increase in fibre content and fibre length. Maximum improvement in liquefac-

tion resistance is found to be 280% for a sand sample reinforced with 1% fibre,

18 mm long, at relative density of 40% and confining pressure of 50 kPa.

Confining pressure has a considerable effect in increasing the resistance to

liquefaction of sand. The liquefaction resistance of sand increases with an

increase in relative density. The effect of reinforcement in medium sand


samples is found to be more significant than that of loose samples (Noorzad and

Amini 2014).

23. The UU triaxial compression test results indicate that the inclusion of PET

fibres (length ¼ 50 mm; diameter ¼ 0.015 mm) influences the internal friction

angle and the cohesion intercept of the silty soil (classified as MH). Greater

fibre contents result in a lower internal friction angle and greater cohesion

intercept. Changes in the friction angle could be attributed to a reduction in the

number of contact points between the soil particles due to the presence of fibres

and the greater cohesion intercept due to increase in apparent cohesion of the

soil particles and fibres (Botero et al. 2015).

24. In the UU triaxial compression test, addition of PP fibres to clay increases both

peak and post-peak deviator stresses and increases the ductility of soil. The

deviator stress at failure decreases with increasing water content, and the

influence of fibres diminishes at higher water content due to the higher water

content facilitating pullout failure at the fibre-soil interface. The addition of

lime alters not only the soil properties (significant increase in shear strength)

but also the soil-fibre interface behaviour. The hydrated lime developed on the

surface of the fibres increases the surface roughness of the fibre, increasing the

pullout resistance and thereby increasing the mobilized tension within the

fibres. Moreover, a reduction of free water within the soil structure by addition

of lime also increases the fibre-soil friction resistance (Gelder and Fowmes

2016).

Example 3.2

Polyester fibres are available in the following two forms: (i) L¼ 12 mm,

D¼ 0.075 mm; and (ii) L¼ 15 mm, D¼ 0.1 mm, where L and D are length and

diameter of fibres, respectively. If a sandy soil is to be reinforced, which form of the

fibres should be recommended for strength improvement? Justify your answer.

Solution

From Eq. (2.1), the aspect ratio of fibres is

ar ¼ L

D

For case (i),

ar ¼ L

D¼ 12

0:075¼ 160

For case (ii),

ar ¼ L

D¼ 15

0:1¼ 150


In general, the strength of fibre-reinforced sandy soil increases with increasing

aspect ratio of fibres, so the fibres having length, L¼ 12 mm, and diameter,

D ¼ 0.075 mm, should be recommended for achieving a higher strength.

3.5 Compaction Behaviour

The studies have been carried out to investigate the compaction behaviour of fibre-

reinforced soils by using the compaction tests in accordance with available stan-

dards on unreinforced soil compaction.

Kaniraj and Havanagi (2001) studied the compaction characteristics of Rajghat

fly ash, Delhi silt, mixture of 50% Rajghat fly ash and 50% Delhi silt and mixture of

50% Rajghat fly ash and 50% Yamuna sand with and without random distribution

of PET fibre reinforcement. The values of maximum dry unit weight (γdmax) and

optimumwater content (wopt) as determined from standard Proctor compaction tests

are given in Table 3.6.

In Table 3.6, you may notice that except in fly ash, in silt and other fly ash-soil

mixtures, the fibres have no significant effect on γdmax and wopt. In the case of fly

ash, as the fibre content increases, the value of γdmax of fly ash increases, whereas

the value of wopt of fly ash decreases.

When the cohesive-frictional soil is reinforced with sisal (natural) fibres, the

fibre inclusion reduces the dry unit weight of soil due to low specific gravity (0.962)

of sisal fibres. The increase in fibre content (from 0.25 to 1%) and fibre length (from

10 to 25 mm) also reduces the dry unit weight of the soil; the variation is linear for

both cases. The dry unit weight of reinforced soil ranges from 16.98 to 17.75 kN/m3

. The initial inclusion of fibres in soil causes an increase in optimum water content,

but a further increase in both fibre content and length reduces the optimum water

content. The optimum water content of reinforced soil ranges from 16 to 19.2%

(Prabakar and Sridhar 2002).

Table 3.6 Compaction test results of fly ash, silt and soil mixtures with fibre content (defined as

the ratio of weight of fibre solids to sum of weights of soil solids and fly ash solids), pf¼ 1%, for

the reinforced cases (After Kaniraj and Havanagi 2001)

Soil type

Maximum dry unit weight,

γdmax (kN/m3)

Optimum water content,

wopt (%)

Unreinforced Reinforced Unreinforced Reinforced

Fly ash 10.52 11.27 36.5 31.7

Silt 17.66 17.60 14.0 14.5

Mixture of 50% fly ash and 50% silt 13.54 13.90 22.6 23.0

Mixture of 50% of fly ash and 50%

sand

13.64 13.60 22.6 23.5

Note: For fly ash reinforced with fibres ( pf¼ 0.5%), γdmax¼ 11.06 kN/m3 and wopt¼ 33.1%

3.5 Compaction Behaviour 77

The standard Proctor tests conducted by Gosavi et al. (2004) indicate that the

optimum water content of black cotton soil increases, and its maximum dry unit

weight decreases by inclusion of glass fibres up to 2% fibre content. However, the

trends are reversed on further increase of fibre content.

The compaction test results reported by Miller and Rifai (2004) for PP fibre-

reinforced medium plasticity soil indicate that for the standard compactive effort,

the optimum water content varies within approximately 4.6% of the value for the

unreinforced soil, while the maximum dry unit weight increases by about 1%,

reaching a peak at a fibre content of 0.8%. The trends for modified compaction

effort are similar. A comparison between the results of the two compaction efforts

shows that the dry unit weight was maximized at fibre contents of 0.8% and 0.6%

for standard and modified efforts, respectively. The variations in the maximum dry

unit weight and optimum water content are less than 5%. Therefore, the changes in

compaction behaviour of the soil due to fibre inclusion are considered insignificant.

Kumar and Singh (2008) observed that the addition of 0.5% of PP fibres resulted

in a decrease in optimum water content and maximum dry unit weight of fly ash by

6.8% and 2.8%, respectively.

For a given compactive effort, the maximum dry unit weight of PP crimped

fibre-reinforced sand decreases with increasing fibre content, whereas the optimum

water content (around 10%) is independent of the amount of fibres (0–0.5%). More

compaction energy may be necessary to produce specimens with higher fibre

contents at a given dry unit weight (Ibraim et al. 2010).

Mirzababaei et al. (2013) studied the compaction behaviour of carpet waste

fibre-reinforced clay soil. As seen in Fig. 3.15, increasing the fibre content leads to a

reduction in the maximum dry unit weight and an increase in optimum water

content. A decrease in maximum dry unit weight is primarily attributed to the

lower specific gravity (1.14) of fibres (100% nylon) compared to the specific gravity

of soil solids (2.68).

Water content, w (%) 5 10 15 20 25 30 35 40 45

10

1214

16

18

20

Dry

uni

t wei

ght, γ d

(kN

/m3 ) Unreinforced soil

fp = 1%3%

5%

Fig. 3.15 Effect of fibre content on compaction curves for carpet waste fibre-reinforced clay soil

(a combination of 90% natural clay (CL as per unified soil classification system) from the

Northwest region of UK and 10% sodium activated bentonite) (Adapted from Mirzababaei et al.

2013)


For a uniform mixing of fibre and clay, the natural moisture content of clay may

be increased. The moisture content that facilitates easy and uniform mixing is called

the optimum mixing moisture content (OMMC). For the clay and PP fibres used in

the study by Gelder and Fowmes (2016), the OMMC was found to be 26%,

although the natural moisture content of the clay was about 16%.

PP fibre inclusions within the clay resist the compactive effort, forming an

interlocked structure. As a result, the optimum water content of clay increases,

and its maximum dry unit weight decreases with increasing fibre content from 0 to

0.75%, without any significant change in the compaction behaviour in terms of the

shape of the compaction curve (Gelder and Fowmes 2016).

The following points regarding the compaction behaviour of fibre-reinforced

soils are worth mentioning:

1. Incorporation of fibres within the soil tends to decrease the maximum dry unit

weight and increase the optimum water content of the fibre-reinforced soil,

mainly due to increased voids caused by fibre separation of the soil particles.

The increased compactive effort, from standard to modified compaction, results

in increased strength of fibre-reinforced soil and somewhat improved interfacial

fibre-soil bond (Hoover et al. 1982).

2. Both the porosity and amount and type of compaction affect the response of a

fibre-reinforced soil. The greater the fibre content, the greater compactive effort

requires maintaining a given porosity. On the other hand, an increase in

compactive effort also results in greater fibre entanglement and distortion,

which also affect the response of a fibre-reinforced soil (Gray and Al-Refeai

1986).

3. The presence of randomly oriented PP fibres in cohesionless soil creates a higher

resistance to compaction than multioriented inclusions (Lawton and Fox 1992).

4. Inclusion of 10% of tyre buffings (length ¼ 4–10 mm; diameter ¼ 0.3–1.5 mm)

reduces the unit weight of the clay. The compaction process causes a preferential

alignment of fibres in directions parallel to the compaction plane. This prefer-

ential orientation is favourable for resisting the desiccation cracking and tensile

stresses that may exit on slopes. The efficiency of compaction does not change at

standard compaction energy but decreases when modified compaction energy is

used. This causes a decrease in the slope of the line of optimums. Hence the unit

weight of the reinforced clay is less sensitive to the compaction water content

compared with clay alone. This may be advantageous in the field, as water

content is difficult to control (Ozkul and Baykal 2006).

5. The inclusion of PP fibres in Brickies sand (classified as SP) causes a significant

reduction in the maximum dry unit weight with a minor increase in optimum

water content (Shukla et al. 2015).

6. The addition of lime to clay along with PP fibres reduces the maximum dry unit

weight dramatically to 16.48 kN/m3 and increases the optimum water content to

21%. The percentage change in the maximum dry unit weight and optimum

water content is�15.58% and +75%, respectively, compared with the values for

clay with no additives. The changes with respect to fibre-only reinforced soil are

3.5 Compaction Behaviour 79

�8.5% and +27%. In addition, the inclusion of lime affects the compaction

behaviour, as indicated by flattening of the compaction curve for soil with lime

(Gelder and Fowmes 2016).

7. As different fibres absorb varying amount of water during the compaction test,

the compaction test parameters may differ accordingly. In general, the absorp-

tion of water by fibres increases the optimum water content of soil.

8. The trend in the change of compaction test parameters due to fibre inclusions as

reported by the researchers is not very consistent. For example, Fletcher and

Humphries (1991) and Nataraj and McManis (1997) found the optimum water

content and the maximum dry unit weight of soil to slightly decrease and

increase, respectively. This contradicts the observations by Mirzababaei et al.

(2013) and Gelder and Fowmes (2016). Thus, there is still a need of further

research on investigating the effect of various types of fibres and different fibre

contents on compaction characteristics of soils and other similar materials such

as fly ashes.

3.6 Permeability and Compressibility

Based on some limited tests, the author has experienced that it is difficult to get the

consistent results for the permeability (i.e. hydraulic conductivity) behaviour of

fibre-reinforced soils with varying fibre and soil parameters. In general, for a given

fibre content, the hydraulic conductivity increases with increasing length of the

fibres. The effect of fibre content on the permeability depends greatly on the density

of the reinforced soil as well as the confinement pressure; thus both increasing and

deceasing trends can be seen.

The investigation carried out by Maher and Ho (1994) shows that with an

increase in the fibre content, the hydraulic conductivity of normally consolidated

fibre-reinforced kaolinite clay (with water content close to the compacted optimum

value of 25%) increases for the fibre types (PP fibres, glass fibres and softwood pulp

fibres) and lengths (0.55–25.4 mm) used. In practical applications, however, the

fibre content should be such that increasing volume stability is achieved without

exceeding the allowable limit on hydraulic conductivity.

Embankment dams and other water-retaining structures are often prone to

seepage erosion in the form of piping. If fibres are added to soil in making these

structures, their presence can affect the piping behaviour of soil. Babu and

Vasudevan (2008b) carried out a number of experiments for determining seepage

velocity and piping resistance of sand, red soil and mixture of sand and red soil

(50% sand + 50% red soil) mixed randomly with coir fibres (length ¼ 40–60 mm;

average diameter ¼ 0.025 mm). The fibre contents varied from 0.25 to 1.5%. The

tests results indicate the following:

1. Inclusion of coir fibres in soil reduces the lifting of individual soil particles when

water flows in the upward direction through the soil mass and increases the


critical hydraulic gradient (i.e. the gradient at which piping failure occurs). Thus,

the piping failure due to lifting of soil particles is found to occur in fibre-

reinforced soil at high hydraulic gradients, whereas the unreinforced soil fails

at comparatively low hydraulic gradients. This is clearly observed for fibre-

reinforced red soil and also for fibre-reinforced sand-red soil mixture.

2. An increase in fibre content causes a decrease in seepage velocity and an

increase in piping resistance of all three types of soil. The least value of seepage

velocity is observed for fibre length of 50 mm. If the length of fibre is low, say

25 mm, the fibre content has no effect on discharge, and similarly, if the fibres

are longer than 75 mm, seepage is not reduced substantially.

To investigate the effect of PP and PET fibres on the piping behaviour of silty

sand, Das and Viswanadham (2010) carried out the laboratory experiments by

developing a one-dimensional piping test apparatus, which simulates the upward

seepage through a soil with and without fibres. The test considered the fibre

contents of 0.05, 0.1 and 0.15% with two different fibre lengths of 25 and 50 mm.

The test results suggest the following:

1. The inclusion of PP and PET fibres reduces seepage velocity and improves the

piping resistance of silty sand for fibre content of 0.1% and fibre length of

50 mm. Of the two fibre types, PP fibres are found to be more effective in

improving the piping behaviour of soil. For PET fibres, because of a higher

specific gravity, the number of fibres reduces for a given fibre content.

2. The seepage velocity increases almost linearly with hydraulic gradient i (seeSec. 1.3 for definition) during the initial stage, indicating a laminar flow until the

critical hydraulic gradient ic is reached. Beyond ic, the seepage velocity is

observed to increase catastrophically.

3. The permeability of silty sand decreases as a result of fibre inclusion. This

observed behaviour could be caused by a reduction in the porosity of soil by

the fibres blocking flow channels. This is essentially due to the fact that the fibres

contribute to the volume of soil solids, leading to reduction in the void ratio.

4. The fibres not only restrict the flow of water but also held the soil particles and

resist their movement under an increasing hydraulic gradient.

5. Figure 3.16 shows the variation of critical hydraulic gradient and piping resis-

tance against the fibre content. It is noticed that, irrespective of fibre length or

fibre type, the piping resistance increases with an increase in fibre content.

Hence the fibres can be mixed into soil for making embankment dams and

other water-retaining structures more resistant to piping erosion.

6. A higher fibre content, say greater than 0.15% for PP and PET fibres, may cause

accumulation of a cluster of fibres in one location, resulting in more flow of

water and reduction in piping resistance.

Kaniraj and Havanagi (2001) conducted the one-dimensional consolidation tests

on Rajghat fly ash, mixture of 50% Rajghat fly ash and 50% Delhi silt and mixture

of 50% Rajghat fly ash and 50% Yamuna sand with and without random distribu-

tion of PET fibre reinforcement. The specimens were compacted statically at their

3.6 Permeability and Compressibility 81


maximum dry unit weight-optimum water content state. Figure 3.17 shows the

relationship between the void ratio e and the logarithm of the effective vertical

stress log10σ0v for unreinforced and fibre-reinforced fly ash specimens. Table 3.7

presents the test values of compression index Cc, recompression index Cr and

coefficient of consolidation cv. The test results show that the fibre inclusions

0 0.05 0.10 0.15 0.201.0

1.5

2.0

2.5

3.0

3.5

4.0

6

9

12

15

18

22

25


Crit

ical

hyd

raul

ic g

radi

ent,

i c

Pipi

ng re

sist

ance

(N)

PP; L = 50 mm

PP; L = 25 mm

PET; L = 50 mm

PET; L = 25 mm

Fig. 3.16 Variation of critical hydraulic gradient and piping resistance of soil with fibre content

(Adapted from Das and Viswanadham 2010)

)kPa(vs¢1 10 100 1000 10000

0.8

0.9

1.0

1.1

1.2

e

Unreinforced fly ash

Fibre-reinforced fly ash

Fig. 3.17 e� log10σ0v curves for unreinforced and fibre-reinforced fly ash specimens (Adapted

from Kaniraj and Havanagi 2001)


increase the value of Cc and cause accelerated consolidation to some extent,

especially of reinforced fly ash, as indicated by the higher values of cv.Expansive soils/clays change volume when subjected to variation in water

content, and any such change causes damages to foundations of structures, such

as buildings, bridges and pavements. In recent years, the researchers have tried to

study the effect of fibre inclusion on swelling behaviour of such soils in terms of

swell potential and swelling pressure. The free swell method is generally adopted to

evaluate both swell potential and swelling pressure. During the swell test in a

one-dimensional oedometer cell, the soil specimen is allowed to swell freely

under a seating load. The maximum swell that the specimen achieves is called

the swell potential and is presented as a percentage of the initial thickness H of the

soil specimen. Load increments are then added to bring the soil specimen to its

initial void ratio. The pressure that brings the soil specimen to its initial void ratio is

defined as the swelling pressure of the soil.The effect of fibre reinforcement on swelling behaviour of soil can be expressed

as the swelling potential ratio (SPR), which is defined as a ratio of the swelling

potential of the reinforced soil specimen (ΔH/H )R to the swelling potential of the

unreinforced soil specimen (ΔH/H )U, where ΔH is the change in the thickness of

the soil specimen. Thus,

SPR ¼ΔHH

� �R

ΔHH

� �U

ð3:13Þ

Al-Akhras et al. (2008) investigated the effect of two types of fibres (synthetic

nylon and natural palmyra) on the swelling properties of three types of clayey soils

(classified as CH, CH and CL) by conducting swell tests in a one-dimensional

oedometer cell. The test results indicate the following:

1. Clayey soils mixed with fibres show significantly lower swelling pressure and

swell potential in comparison with the same clayey soils without fibres

(Fig. 3.18).

Table 3.7 One-dimensional consolidation test results for fly ash and soil mixtures with fibre

content (defined as the ratio of weight of fibre solids to sum of weights of soil solids and fly ash

solids), pf¼ 1%, for the reinforced cases (After Kaniraj and Havanagi 2001)

Soil type


Cc Cr

cv (m2/

year) Cc Cr

cv (m2/

year)

Fly ash 0.072 0.017 238–299 0.123 0.022 248–347

Mixture of 50% fly ash and 50%

silt

0.123 0.021 254–290 0.148 0.022 224–288

Mixture of 50% of fly ash and 50%

sand

0.093 0.016 291–315 0.164 0.025 275–378


2. Clayey soils mixed with palmyra fibres show substantially lower swelling

pressure and swell potential in comparison with clayey soils mixed with nylon

fibres at the same fibre content.

3. Clayey soils mixed with fibres with aspect ratio of 25 show lower swelling

pressure in comparison with clayey soils mixed with fibres with aspect ratio

of 100.


ra = 100

ra = 75

ra = 50

ra = 25

0 1 2 3 4 5 60

5

10

15

20

25Sw

ell p

oten

tial(

%)

Fibre content, fp (%)0 1 2 53 4

0

500b

aSw

ellin

g pr

essu

re(k

Pa) 400

300

200

100

ra = 100

ra = 75

ra = 50

ra = 25

Fig. 3.18 Effect of nylon fibres on: (a) swell potential; (b) swelling pressure of clayey soil

(classified as CH with liquid limit of 78% and plasticity index of 43%) (Adapted from

Al-Akhras et al. 2008)


4. The impact of the inclusion of fibres in clayey soils increases with increasing

clay fraction of the clayey soil.

Babu et al. (2008b) carried out consolidation and swell tests on coir fibre-

reinforced black cotton soil, which is an expansive soil. The test results indicate

that swelling is reduced by about 40% when the fibre content is increased from 0.5

to 1.5%, and the compression index (see Table 3.8) decreases by about 35% for a

fibre content of 1.5%. Thus the coir fibres are suited for controlling the swelling of

black cotton soil, and hence the excessive settlement of structures built on such

compacted soil deposits can be reduced considerably.

Viswanadham et al. (2009a, b) performed swell-consolidation tests in a conven-

tional oedometer (diameter ¼ 75 mm; thickness ¼ 25 mm) on expansive soil

(classified as CH) reinforced with PP fibres using varying fibre contents

(0.25–0.5%) and aspect ratios (15, 30 and 45). The test results indicate that an

inclusion of PP fibres reduces the heave of the soil. Heave is reduced more at lower

aspect ratios than at higher aspect ratios. Swelling decreases with increasing fibre

content for all aspect ratios. Reduction in swelling is rapid up to aspect ratio of 15 at

all fibre contents. When the aspect ratio is low, even small fibre content is found

effective. Swelling pressure decreases as a result of fibre inclusion. Reduction in

swelling can be attributed to replacement of swelling soil by fibres and resistance

offered by fibres to swelling through clay-fibre contact. When swelling of the soil

occurs, the flexible fibres in the soil are stretched, and hence the tension in fibres

resists the further swelling. Resistance offered by the fibres to swelling depends

upon the soil-fibre contact area. When the long fibres are mixed randomly, they tend

to twist or fold. This reflects in the form of loss of effective soil-fibre contact area

for restraining swelling.

The following points regarding permeability and compressibility of fibre-

reinforced soils are worth mentioning:

1. Use of the fibres decreases freeze-thaw volumetric change on the order of 40%

as compared with the unreinforced soil. When the fibre-reinforced soil is mod-

ified with a low cement content, freeze-thaw volumetric expansion is eliminated,

indicating an extremely stable reinforced soil (Hoover et al. 1982).

2. The experimental study conducted by Miller and Rifai (2004) indicates that the

PP fibre inclusion increases the desiccation crack reduction significantly due to

increased tensile strength of the medium plasticity soil (classified as CL) due to

Table 3.8 Compression

index of unreinforced and coir

fibre-reinforced black cotton

soils (After Babu et al. 2008b)

Fibre content, pf (%) Compression index, Cc

0 0.51

0.5 0.43

1 0.40

1.5 0.33

Note: For coir fibres, length, L¼ 15 mm, and diameter,

D¼ 0.25 mm


fibre inclusion. The optimum fibre content for achieving the maximum crack

reduction and maximum dry unit weight, while maintaining the acceptable

hydraulic conductivity, is between 0.4 and 0.5%.

3. The initial void ratio is more for unreinforced fine sand than that for fine sand

reinforced with plastic waste chips/fibres (polymer ¼ PET, specific gravity ¼1.33, length ¼ 6 mm, width ¼ 0.2 mm) because the plastic fibres occupy the

voids within the soil solids. The compressibility of soil reduces as the fibre

content increases; this is indicated by a decrease in the slope of void ratio versus

logarithm of effective stress curve with an increase in fibre content. As the fibre

content in the sand is increased from 0.5 to 1%, the permeability of sand

decreases by two times that of unreinforced sand (Manjari et al. 2011).

4. The permeability test using the falling-head permeameter shows that increasing

fibre content of waste tyre yarn fibres initially increases the hydraulic conduc-

tivity of fine-grained soil, and when it crosses 0.6% limit, it decreases (Saghari

et al. 2015).

3.7 California Bearing Ratio

The bearing capacity ratio (CBR) of fibre-reinforced soil has been studied by

several researchers by conducting California bearing ratio (CBR) test. For the

analysis and design of fibre-reinforced soil bases/subbases/subgrades of the pave-

ments, the effect of fibres on the CBR value is generally represented by the loadratio, which is a nondimensional parameter, defined as

LR ¼ QR

QpU

ð3:14Þ

where QpU is the peak piston load on unreinforced soil and QR is the piston load on

fibre-reinforced soil corresponding to the piston penetration ρ(¼ρpU) on

unreinforced soil at the peak piston load QpU.

Note that in Eq. (3.14), QR can be the piston load on the reinforced soil at any

selected/permissible penetration of the piston as required for the safety of the

pavement structure. For QR¼QpR (peak piston load on reinforced soil) at ρ¼ ρpR(peak piston penetration), Eq. (3.14) reduces to peak load ratio (PLR) as

PLR ¼ QpR

QpU

ð3:15Þ

The effect of fibres on the CBR value can also be represented by the CBRimprovement factor ICBR, or normalized CBR value CBRR, defined as


ICBR ¼ CBRR � CBRU

CBRU

¼ CBRR

CBRU

� 1 ð3:16Þ

CBRR ¼ CBRR

CBRU

ð3:17Þ

where CBRU is the CBR value of the unreinforced soil, and CBRR is the CBR value

of the reinforced soil.

The CBR tests carried out by Lindh and Eriksson (1990) show that the wet sand

reinforced with 48-mm long plastic fibres does not offer a CBR value significantly

higher than the sand alone at a deformation of 2.54 mm. However, the sand

specimens containing fibres show a continuously rising curve in the stress-

deformation diagram, unlike sand without fibres, which shows clear fractures

(Fig. 3.19).

Tingle et al. (2002) have reported that use of fibres improves the CBR of the sand

from 6 to 34% over the unstabilized sand shoulder at similar depths. The improve-

ment in load-bearing capacity of the fibre-stabilized sand can be attributed to the

confinement of the sand particles by the discrete fibres. When the fibres are mixed

into the sand, the fibres develop friction at interaction points with the particles that

resist rearrangement of the particles under loading. Thus, the primary stabilization

mechanism is the mechanical confinement of the sand. They have also reported that

‘springy or sponge-like’ behaviour is a fundamental property of the fibre-reinforced

soil.

The CBR of black cotton soil increases by about 46% and 55% for aspect ratios

of 250 and 500, respectively, as a result of inclusion of 2% glass fibre. An increased

CBR makes the pavement construction economical by reducing the thickness of

pavement layers (Gosavi et al. 2004).

2.54 5.0800

1.25

2.5

3.75

5.0

6.25

7.5

Deformation, d (mm)

Stre

ss, s

(MPa

)

fp = 0.5%, w = 8%

fp = 0%, w = 8%fp = 0.25%, w = 8%

fp = 0%, w = 10%

Fig. 3.19 CBR test results on wet sand with and without fibres (water content, w ¼ 8–10%)

(Adapted from Lindh and Eriksson 1990)

3.7 California Bearing Ratio 87

Yetimoglu et al. (2005) performed the laboratory CBR tests to investigate the

load-penetration behaviour of a clean sand fill reinforced with randomly distributed

discrete PP fibres (length¼20 mm; diameter¼ 0.50 mm) overlying a high plasticity

inorganic clay with a nonwoven geotextile layer at the sand-clay interface as a

separator. Figure 3.20 shows the effect of fibre content on the peak load ratio (PLR)

for the fibre-reinforced sand fill. It is noticed that the PLR value increases with an

increase in fibre content and becomes approximately five times as high as that of

unreinforced sand. The investigation also shows that the initial stiffness (i.e. the

slope of the load-penetration curve) is not significantly changed by incorporating

the fibres in sand. The penetration values at which the peak loads are mobilized tend

to increase with increasing fibre content. It is also observed that increasing fibre

content increases the brittleness of the fibre-reinforced sand as indicated by a higher

loss of post-peak penetration resistance (strength). Additionally it is observed that

the load-penetration behaviour of the sand reinforced randomly with a small

amount of fibre inclusion is quite similar to that of the sand reinforced systemati-

cally with geotextile layers in a certain pattern.

The experimental study conducted by Kumar and Singh (2008) shows that the

soaked and unsoaked CBR values of fly ash (classified as silt of low compressibility,

ML) reinforced with randomly distributed PP fibres increase with an increase in

0 0.2 0.4 0.6 0.8 1 1.20

1

2

3

4

5

6


Peak

load

ratio

, PLR

Fig. 3.20 Variation of peak load ratio (PLR) with fibre content ( pf) for fibre-reinforced sand

(Adapted from Yetimoglu et al. 2005)


fibre content at a particular aspect ratio (60, 80, 100 or 120). The increments have

been reported to be more up to 0.3% fibre content. Based on the experimental

results, a regression relationship between soaked CBR and fibre content pf rangingfrom 0.1 to 0.5% was presented as

CBR ¼ alnpf þ b ð3:18Þ

where a ¼ 10.102, 11.323, 12.037 and 12.187 and b ¼ 32.394, 35.855, 39.211 and

40.273 for ar ¼ 60, 80, 100 and 120, respectively. Note that the soaked and

unsoaked values of CBR of fly ash were 8.5% and 20.2%, respectively.

In general, the CBR value of reinforced soils continue to increase with both fibre

content and aspect ratio, but mixing soil and fibres is extremely difficult beyond the

fibre content of 1.5%. For soils reinforced with PP fibres (length ¼ 15 mm, 25 mm,

30 mm; diameter ¼ 0.3 mm), the experimental study conducted by Chandra et al.

(2008) suggests that 1.5% fibre content and an aspect ratio of 100 can be considered

optimum values in the case of soils of low compressibility (classified as CL and

ML), whereas 1.5% fibre content with an aspect ratio of 84 is found to be optimum

for silty sand (classified as SM). The CBR values of CL, ML and SM compacted at

standard compaction test parameters were found to be 1.16, 1.95 and 6.20%,

respectively. These values increased to 4.33, 6.42 and 18.03%, respectively, due

to reinforcing the soil at optimum fibre content of 1.5%.

Zaimoglu and Yetimoglu (2012) investigated the effects of randomly distributed

PP fibre reinforcement (length ¼ 12 mm; diameter ¼ 0.05 mm) on the soaked CBRbehaviour of a fine-grained soil (MH, high plasticity soil) by conducting a series of

CBR tests. Figure 3.21 shows a typical variation of soaked CBR with the fibre

content. It is observed that the CBR value increases significantly with increasing

fibre content up to around 0.75% and remains more or less constant thereafter. The

maximum increase in CBR is around 80% (i.e. from approximately 14% for

unreinforced soil to approximately 25% for reinforced soil at a fibre content of

0.75%).

00

0.25 0.5 0.75 1

5

10

15202530


CBR

(%)

Fig. 3.21 Effect of fibre content on the soaked CBR behaviour of fine-grained soil (Adapted from

Zaimoglu and Yetimoglu et al. 2012)


Edincliler and Cagatay (2013) presented experimental results on the improve-

ment of CBR performance of sand by addition of granulated rubber (aspect ratio ¼1) and fibre shaped buffing rubber (aspect ratios of 4 and 8). Mixtures were prepared

at rubber contents of 5, 10, 20, 30 and 40% by weight. The results show that the

addition of 30% (by weight) buffing rubber to sand increases the CBR value of the

reinforced sand, but the addition of granulated rubber decreases it. The use of

buffing rubbers with the highest aspect ratio of eight results in an increase in CBRfrom 8 to 16 (100% increase, while the increase in CBR is from 8 to almost 12 (44%

increase) with inclusion of buffing rubbers having an aspect ratio of 4. Thus use of

the longer fibres causes significant benefit. This happens because the longer fibres

have a large contact area with the soil particles, resulting in more friction/adhesion.

Addition of HDPE plastic waste strips (length¼ 12, 24, 36 mm; width¼ 12 mm;

thickness ¼ 0.4 mm) to industrial wastes (fly ash, stone dust and waste recycled

product) results in an appreciable increase in the CBR value and the subgrade

modulus. Table 3.9 provides the CBR test values. The subgrade modulus values

for fly ash, stone dust and waste recycled product increase from 65 to 525 MPa/m,

127 to 894 MPa/m and 858 to 2078 MPa/m, respectively for 4% strip/fibre content

with an aspect ratio of 3. The significant increases in CBR value and subgrade

modulus indicate that these reinforced industrial wastes can be used in flexible

Table 3.9 Values of California bearing ratio (CBR) for plastic waste fibre-reinforced industrial

wastes (After Jha et al. 2014)

Aspect

ratio, ar

Fibre

content,

pf (%)

CBR(%)

Fly ash (specific

gravity ¼ 2.20; 49%

sand-size particles with

51% fines)

Stone dust (specific

gravity ¼ 2.63;

84% sand and

16% fines)

Waste recycled product

(specific gravity ¼ 2.87;

sand-size particles

without fines)

Unreinforced soil 3.11 6.08 41.85

1 0.25 4.38 8.27 49.88

0.5 9.49 9.73 66.23

1 11.68 14.11 70.17

2 13.87 21.41 74.16

4 19.46 23.36 76.89

2 0.25 7.30 8.56 59.85

0.5 9.98 17.52 71.00

1 12.41 21.90 74.99

2 16.79 24.33 88.08

4 23.31 27.74 88.56

3 0.25 7.54 9.73 60.24

0.5 10.70 22.87 82.58

1 12.65 27.25 88.56

2 17.27 34.30 96.35

4 25.06 42.73 99.27


pavement construction, leading to safe and economical disposal of the wastes

(Choudhary et al. 2014; Jha et al. 2014).

Sarbaz et al. (2014) conducted the CBR tests under dry and submerged condi-

tions on fine sand (SP) reinforced with plain date palm fibres (see Table 2.1 for

properties) as well as with bitumen-coated date palm fibres. The test results indicate

the following:

1. Adding 0.5–1% fibres enhances the CBR strength significantly by up to 56%

compared to unreinforced sand. However, this effect gradually diminishes at

higher fibre contents. For example, the CBR strength at 2% fibre content

decreases slightly. Obviously, the presence of fibres in the soil more than what

is required for optimum reinforcement can substitute the soil particles with

weaker materials, thereby reducing the bearing capacity of the soil.

2. Soil reinforced with longer fibres has higher CBR strength than soil reinforced

with shorter fibres. This can likely be attributed to the more mobilized frictional

resistance around the fibres, and, consequently, higher tensile stresses are devel-

oped in the fibres.

3. The CBR strength of soil reinforced with bitumen-coated fibres is slightly lower

compared with that for soil reinforced with plain fibres. This is because of the

reduction of frictional resistance between fibres and soil particles as result of

bitumen coating on fibres. With an increase in fibre length, the effect of coating

of fibres with bitumen decreases. For example, in soil specimens reinforced with

1% fibre of 40-mm length, coating of fibres with bitumen causes a negligible

reduction.

4. Submergence of unreinforced and reinforced soil specimens causes the CBRstrength to decrease considerably.

5. Dry and wet conditions and semi-saturation condition have no effect on CBRstrength.

The following points regarding the CBR behaviour of fibre-reinforced soils are

worth mentioning:

1. The CBR value increases nearly linearly to a maximum of six times that of

unreinforced soil at fibre content of 0.8% for 1.5-in. long PP fibres. The CBR test

values indicate that inclusion of fibres is most effective in sandy soils and less

effective in the fine-grained soils (Hoover et al. 1982).

2. The addition of PP fibres improves the bearing capacity of the soil by an increase

in CBR values of as much as 133% (Fletcher and Humphries 1991).

3. The inclusion of fibres increases the CBR value of dune sand, and the improve-

ment in the CBR can be maintained over a larger penetration range than with

unreinforced sand (Al-Refeai and Al-Suhaibani 1998).

4. Addition of waste HDPE plastic strip inclusions (lengths¼ 12, 24, 36 mm; width

¼ 12 mm; thickness ¼ 0.45 mm) in the stone dust/fly ash overlying saturated

clay subgrade results in an appreciable increase in the CBR value and the secant

modulus for strip content up to 2%. Reinforced stone dust is more effective than


reinforced fly ash overlying saturated clay in improving the behaviour of the

system (Dutta and Sarda 2007).

5. The PP plastic bag waste fibre-reinforced stabilized silty soil meets the require-

ments as subbase and base course materials in terms of its CBR values. The CBRvalue of the soil increases up to 3.6 times by mixing lime and rice husk ash.

However, the CBR value increases considerably up to 8.7 times by adding plastic

waste fibres (length ¼ 20–30 mm; width ¼ 2–2.5 mm). The optimum fibre

content is found to be in the range of 0.4 to 8% (Muntohar et al. 2013).

6. Improvement in CBR value is five times for clay and three times for fly ash with

the addition of tire crumbles (dust or powered waste material produced during

the process of tire retreading, equivalent to poorly graded sand classified as SP).

The CBR value of any mix increases with an increase in the content of tire

crumbles up to a certain limit of the tire crumbles content, approximately 5%,

known as the optimum content, after which further improvement in CBR value is

not significant. The CBR of fly ash-tire crumble mix is relatively greater as

compared to the CBR of clay-tire crumble mix (Priyadarshee et al. 2015).

7. The CBR value of high compressibility clayey soil (CH) increases from 4.70 to

7.75% as a result of inclusion of about 2% human hair fibre (length ¼ 25 mm;

diameter ¼ 0.05 mm). The increase in CBR may be caused by improved

interfacial adhesion between soil particles and hair fibres. Both the undrained

shear strength and the CBR reduce when the fibre content is more than 2%. It

appears that a higher fibre content leads to a reduction in interfacial adhesion

between soil particles and fibres in the reinforced soil. Thus 2% fibre content is

the optimum quantity to enhance undrained shear strength and CBR of clayey

soil (Butt et al. 2016).

3.8 Load-Carrying Capacity

Load-bearing capacity and settlement characteristics of fibre-reinforced soil have

been studied by several researchers by conducting plate load tests. For the analysis

and design of shallow foundations on fibre-reinforced soil beds, the effect of fibres

on the load-bearing capacity of the footing resting on reinforced soil is generally

represented by the bearing capacity ratio (BCR), which is a nondimensional param-

eter defined as

BCR ¼ qRquU

ð3:19Þ

where quU is the ultimate load-bearing capacity of the unreinforced soil and qR is

the load-bearing pressure on the reinforced soil corresponding to the settlement

ρ(¼ρuU) of the footing resting on unreinforced soil at the ultimate load-bearing

capacity quU.


Figure 3.22 shows the typical load-settlement curves for a soil with and without

fibre reinforcement and illustrates how quU and qR are determined. The procedure

for determination of ultimate load-bearing capacity quR of the reinforced soil and

the corresponding settlement ρuR is also shown in Fig. 3.22.

Note that in Eq. (3.19), qR can be the load-bearing pressure on the reinforced soilat any selected/permissible settlement of the footing as required for the safety of the

specific structure. For qR¼quR at ρ¼ ρuR, Eq. (3.19) reduces to ultimate bearingcapacity ratio as

BCRu ¼ quRquU

ð3:20Þ

Hence it is important to clarify the definition of BCR being used in discussion as

the values obtained from Eq. (3.19) and (3.20) can be quite different. In the author’sopinion, it is better to use Eq. (3.19), considering the same level of settlement levels

in both reinforced and unreinforced cases for describing the benefits of reinforce-

ment in terms of an increase in load-bearing capacity compared to the load-bearing

capacity of unreinforced soil.

The improvement in load-bearing capacity of soil as a result of inclusion of fibre

reinforcement can also be expressed in terms of the ultimate bearing capacityimprovement factor IUBC, defined as

IUBC ¼ ΔququU

¼ quR � quUquU

¼ quRquU

� 1 ¼ BCRu � 1 ð3:21Þ

The factor IUBC basically presents a relative gain in load-bearing capacity of soil

due to inclusion of fibres and is normally expressed as a percentage.

Load-bearing pressure, q

RquUq

Uur

Unreinforced soil


uRq

Rur

Settl

emen

t, r

Fig. 3.22 Typical load-settlement curves for unreinforced and fibre-reinforced soils

3.8 Load-Carrying Capacity 93

As explained earlier, the fibre-reinforced soil with or without cementing material

exhibits ductile behaviour to some extent, which can be described by deformability

index (Di), which is a nondimensional parameter defined as

Di ¼ ρuRρuU

ð3:22Þ

Note that the concept of BCR as defined in Eq. (3.19) was first introduced by

Binquet and Lee (1975a, b) in their study of load-bearing capacity of sand bed

reinforced with metallic reinforcement layers. The concept ofDi has been explained

by Nasr (2014).

A series of laboratory model tests on a strip footing resting on the compacted

uniform sand bed reinforced by randomly distributed PP fibres (50 mm long) and

two different mesh elements (small mesh as 30 mm � 50 mm and big mesh as

50 mm � 100 mm) having the same opening size (10 mm � 10 mm) were

conducted by Wasti and Butun (1996). The test results show that the change in

the ultimate bearing capacity lies between about +40% and �5%; the higher value

is for the big meshes at inclusion contents of 0.1% and 0.15%, and the negative

value is for the fibres and the small meshes at the lowest inclusion content of

0.075%. At all inclusion contents, the use of big meshes brings about the greatest

improvement compared to others. At an inclusion content of 0.15%, the BCRu value

remains the same as for inclusion content of 0.1% for the big meshes and drops

somewhat for the small meshes, suggesting the existence of a possible optimum

amount of inclusion content for the mesh elements between 0.1% and 0.15%.

Unlike the meshes, the BCRu values for the sand with fibres increase linearly as

the inclusion content increases. It is reasonable to assume that the BCRu value for

the fibres will approach an asymptotic upper limit as observed by Gray and

Al-Refeai (1986), Maher and Woods (1990) and Ranjan et al. (1994). It is also

observed that the settlement of the footing at failure increases as the inclusion

content increases. The increase is also seen to be dependent on the type of

reinforcement; the largest one corresponding to the big meshes and the smallest

to the fibres.

The plate load tests conducted by Consoli et al. (2003a) using a 300-mm

diameter plate show that the addition of PP fibres to the low plasticity silty sandy

clayey soil significantly improves the behaviour of soil. A noticeable stiffer

response with increasing settlement of the test plate is observed. This happens

because of a combined effect of the continuous increase in the strength of the soil at

large deformations as observed in the triaxial compression tests.

Consoli et al. (2003b) presented the results of three plate load tests using a

circular plate (300-mm diameter; 25.4 mm thick) on a residual homogeneous soil

stratum (sandy silty red clay, classified as low plasticity clay) as well as on a layered

system formed by two different top layers (300 mm thick) as uniform fine sand-

cement and uniform fine sand-Portland cement-PP fibre mixtures overlying a

residual soil stratum. The test results, as presented in Table 3.10, show that the

addition of fibres to the cemented sand layer over the residual soil stratum keeps the


maximum bearing capacity virtually unchanged but increases settlement at maxi-

mum load and improves the ultimate bearing capacity, when compared to the

cemented sand layer overlying the residual soil stratum. The fibre reinforcement

significantly changes the failure mechanism by preventing the formation of tension

cracks, as observed for the cemented sand layer. Instead, the fibres allow the applied

load to spread through a larger area at the interface between the fibre-reinforced

cemented sand layer and the underlying residual soil stratum as indicated by the

formation of a thick shear band all around the plate during the load test (Fig. 3.23).

Gupta et al. (2006) conducted the model footing tests on the PP fibre-reinforced

poorly graded sand at 50% relative density and presented the pressure-settlement

curves as shown in Fig. 3.24. The tests were conducted on a square footing (150 mm

� 150 mm) in a square test tank of size 1 m � 1 m � 0.35 m (deep). It is observed

that for a given load-bearing pressure, the settlement of unreinforced sand is more

than that of the reinforced sand, and the settlement reduces with an increase in fibre

content. The ultimate load-bearing capacity of the unreinforced and reinforced

sands determined by the method of plotting the load-bearing pressure versus

settlement curve on a log-log graph is given in Table 3.11. It is noted that the

ultimate load-bearing capacity of the fibre-reinforced soil increases with an increase

in fibre content. The percentage increases in the load-bearing capacity of the fibre-

reinforced sand in comparison to unreinforced sand, that is, the value of IUBC is also

given in Table 3.11. A plot of IUBC with fibre content is almost linear, although

direct shear and triaxial compression tests do not show a linear trend for increase in

strength with an increase in fibre content. This suggests that the tests on small

specimens may not be a true indicator for prediction of improved strength of soil as

a result of fibre inclusions.

Table 3.10 Plate load test results for 300-mm circular plate (After Consoli et al. 2003b)

Soil mixtures

Thickness

(mm)

Curing

period

(days)

Load

at

failure

(kN)

Settlement

at failure

(mm) Failure mode

None (plate

directly on the

residual soil)

(Consoli et al.

1998b)

None None Larger

than 40

Larger

than 50

Punching

Sand + 7%

cement layer

300 28 98 8 Tension fissures initiating

on the bottom of sand-

cement layer followed by

punching

Sand + 7%

cement + 0.5%

PP fibres

300 28 91 22 Formation of a shear band

around the plate border,

transferring a higher load

to a larger area of the

residual soil underlying the

cement-stabilized fibre-

reinforced soil layer


300 mma

b

Load Circular test plate

Sand-cement layer

Residual soil stratum

Tension fissure

300 mm

300 mm

Load

Sand-cement-fibres layer

Residual soil stratum

Shear bands

Circular test plate

300 mm

Fig. 3.23 Failure modes for treated soil layer overlying the residual soil stratum: (a) sand-cement

layer; (b) sand-cement-fibre layer (Adapted from Consoli et al. 2003b)

0 100 200 3000

2

4

6

8

10

12

14

Load-bearing pressure, q (kPa)

Settl

emen

t, r

(mm

)

Unreinforced sand

Fibre content,fp = 0.20%

0.10%0.05%

Fig. 3.24 Load-settlement curves for PP fibre-reinforced poorly graded sand at different fibre

contents (Adapted from Gupta et al. 2006)


A series of laboratory model footing tests have been carried out by Hataf and

Rahimi (2006) to investigate the load-bearing capacity of sand reinforced randomly

with tire shreds of rectangular shape (widths of 20 and 30 mm with aspect ratios of

2, 3, 4 and 5). The shred contents used were 10, 20, 30, 40 and 50% by volume of

the dry sand. The results show that addition of tire shreds to sand increases the BCRvalue from 1.17 to 3.9. The maximum BCR value is obtained for the shred content

of 40% and shred dimensions of 30 mm by 120 mm.

Kumar and Singh (2008) conducted plate load tests on prepared fly ash subbases

in test pits with and without fibre reinforcement. It is observed that the modulus of

subgrade reaction ks increases by including the fibres randomly in fly ash and fly

ash-soil (poorly graded fine sand (SP)) mixes. The value of ks at 0.2% fibre content

increases by 15.47, 21.4 and 51.2% for fly ash, fly ash + 15% soil and fly ash +25%

soil, respectively.

Consoli et al. (2009) carried out the plate load tests on unreinforced uniform fine

sand (SP) and this sand reinforced with PP fibres (24 mm long, 0.5% by dry weight),

compacted at relative densities (Dr) of 30, 50 and 90%, using a 300-mm diameter

circular rigid steel plate. The test results indicate that the load-settlement behaviour

of sand is significantly governed by the fibre inclusion, changing the kinematics of

failure. The best performance was obtained for the densest (Dr ¼ 90%) fibre-sand

mixture, where a significant change in the load-settlement behaviour was observed

at very small (almost zero) displacements. However, for the loose to medium dense

sand (Dr ¼ 30% and 50%), significant settlements (50 mm and 30 mm, respec-

tively) were required for the differences in the load-settlement responses to appear.

The settlement required for this divergence to occur could best be represented using

a logarithmic relationship between settlement and relative density. The overall

behaviour seems to support the argument that inclusion of fibres increases strength

of sandy soil by a mechanism that involves the partial suppression of dilation and

hence produces an increase in effective confining pressure and a consequent

increase in shear strength.

Falorca et al. (2011) carried out plate load tests on randomly distributed mono-

filament PP fibre-reinforced silty sand for small displacements and relatively low

load levels using a semi-rigid circular plate, 300 mm in diameter. The fibres were

very fine (fibre diameter of the order of 10 μm). Long fibres (75 mm long), that is,

fibres with a high aspect ratio, were used, because they were expected to be more

Table 3.11 Effect of increase in fibre content on ultimate load-bearing capacity of poorly graded

sand (Adapted from Gupta et al. 2006)

Fibre

content

(%)

Ultimate load-bearing

capacity (kPa)

Increase in load-bearing capacity in comparison to

unreinforced sand* as a result of fibre inclusions, that is,

IUBC (%)

0 85*

0.05 100 17.6

0.1 115 35.3

0.2 140 64.7


effective for soil reinforcement as shown by several past studies. Fibre content was

varied from 0 to 0.5%. The reinforced soil was compacted by a 4 t vibratory roller

with six passes in lift thicknesses of 200 mm to construct a trial embankment (50 m

long, 10 m wide and 0.6 m high), divided into five different sections, each with

different reinforcement characteristics. Both monotonic loading and load-unload

cycles were adopted. Each load level was applied for at least 10 min before

measurements were taken. The modulus of subgrade reaction ks varied from

170 MPa/m for unreinforced soil to 208 MPa/m for fibre-reinforced soil with

corresponding Young’s modulus of elasticity from 130 MPa to 115 MPa. The

Young’s modulus decreases with an increase in fibre content, this reduction being

more pronounced for thinner fibres. The test results show that the soil reinforced

with the thinner fibres is the more compressive one. Although the reinforced soil is

more compressible than unreinforced soil, the reinforced soil shows a considerably

large recovery as indicated during repeated loading and unloading. Note that an

increase in fibre content affects the physical properties of the compacted soil by

essentially increasing the void ratio.

Example 3.3

Consider the following values of ultimate bearing capacity obtained from a plate

load test on unreinforced and fibre-reinforced soils:

For unreinforced soil, quU¼ 85 kPa

For fibre-reinforced soil, quR¼ 140 kPa

Determine the ultimate bearing capacity ratio and ultimate bearing capacity

improvement factor. What does this factor indicate?

Solution

From Eq. (3.20), the ultimate bearing capacity ratio is

BCRu ¼ quRquU

¼ 140

85� 1:65

From Eq. (3.21), the ultimate bearing capacity improvement factor

IUBC ¼ quRquU

� 1 ¼ BCRu � 1 ¼ 1:65� 1 ¼ 0:65 or 65%

This value of IUBC indicates that inclusion of fibres causes 65% increase in the

ultimate bearing capacity of soil.

3.9 Other Properties

The behaviour of fibre-reinforced soils has also been studied by conducting tests

other than those presented in the previous sections. Such tests are Brazilian/indirect/

splitting tensile strength tests, ring shear tests, bender element tests, resonant


column tests, torsional shear tests, etc. Some key findings of the studies based

mainly on these tests as well as some additional characteristics are summarized

below:

1. The inclusion of natural and glass fibres has a significant effect on the dynamic

response of a uniform dune sand, namely, shear modulus and damping ratio.

Both the shear modulus and the damping ratio increase approximately linearly

with an increasing amount of fibres to about 4%, then they tend to approach an

asymptotic upper limit at approximately 5% of fibre content by weight. At higher

fibre content, the reinforcing or stiffening effects are offset by a decrease in

composite density and a dilution or loss of interparticle friction between the sand

particles themselves. An increase in fibre aspect ratio results in more effective

fibre contribution to the dynamic response of sand, that is, shear modulus and

damping ratio. An increase in fibre modulus results in increased fibre contribu-

tion to shear modulus of fibre-reinforced sand, whereas the effect of fibre

modulus on damping ratio is insignificant. The dynamic response of sand

reinforced with vertically oriented fibres is very similar to that of randomly

distributed fibres (Maher and Woods 1990). Noorany and Uzdavines (1989) and

Shewbridge and Sousa (1991) have also reported increase in dynamic shear

modulus as well as liquefaction resistance of cohesionless soils as a result of

fibre inclusion. Note that the observations made by Shewbridge and Sousa

(1991) are based on the cyclic torsional shear strain control tests on large hollow

cylindrical sand specimens reinforced uniaxially and biaxially with 3.175-mm

(0.125-in.) diameter steel rods.

2. The tensile strength of sand increases significantly as a result of fibre inclusion.

Increase in tensile strength is more pronounced for higher fibre contents, longer

fibre lengths and higher cement contents, as seen in Fig. 3.25 (Maher and Ho

1993).

3. The tensile strength of kaolinite clay increases significantly as a result of

inclusion of fibre reinforcement (PP fibres, glass fibres and softwood pulp

fibres). In general, increasing the fibre content increases the tensile strength of

fibre-reinforced kaolinite clay, with the increase being more pronounced at

lower water contents. This happens because increasing water content reduces

the amount of load transfer between the kaolinite particles and the fibres.

Increasing fibre length reduces the contribution of fibres to tensile strength.

Thus for the same amount of fibres present in the reinforced soil, shorter, and

consequently better, dispersed fibres contribute more to tensile strength (Maher

and Ho 1994).

4. The toughness of kaolinite clay beam increases as a result of inclusion of fibres

(PP fibres, glass fibres and softwood pulp fibres) as noticed in flexural load test

using three-point loading method. When a fibre-reinforced kaolinite clay beam is

loaded, the fibres act as crack arrestors and thus increase the toughness (Maher

and Ho 1994).

3.9 Other Properties 99

Fibre content, fp (%)0 1 2 3 4 5 6

0

1

2

3Te

nsile

stre

ngth

, σt(M

Pa)

Cement content, cp = 4%

Fibre length, L = 0.75 in. (19 mm)

Cement content, cp (%)1 72 3 4 5 6

0

0.2

0.4

0.6

Tens

ile st

reng

th, σ

t(M

Pa)

Fibre content,

b

a

fp = 3%

0.8

1

1.2

8

Fibre length, L (in.) =1

0.75

0.5

0.25

No fibre

Fig. 3.25 Effect of glass fibre inclusion on the tensile strength of cement-stabilized standard

Ottawa sand: (a) effect of fibre content; (b) effect of fibre length and cement content (Adapted

from Maher and Ho 1993)


5. An increase in PET fibre content from 0.1 to 0.9% in uniform fine sand

(SP) with an intermediate cement content of 5% causes an average increase

in tensile strength of sand by about 78%. The positive effect of fibre length is

not detected in the splitting tensile tests, clearly indicating the major influence

of confining pressure and the necessity of carrying out triaxial tests to fully

show fibre-reinforced soil behaviour (Consoli et al. 2002).

6. At very small shear strains, the bender element test data obtained by Heineck

et al. (2005) show that the inclusion of PP fibres in soil does not influence the

stiffness at small strains as determined from the stress-strain curves of the

triaxial compression tests.

7. The ring shear tests on PP fibre-reinforced soils (Botucatu residual soil and

uniform Osorio sand) show that there is a continued increase of shear stress

with shear strain, even at the largest strains reached in the ring shear apparatus.

In contrast, for the reinforced bottom ash at lower confining stresses, the shear

stress reaches an approximately constant value of shear stress. Higher strains,

in general, result in greater mobilization of the tensile resistance of the fibres,

which in turn results in an enhanced contribution of the fibres to the stability/

rigidity of the reinforced soil (Heineck et al. 2005; Consoli et al. 2007).

8. The tensile strength (maximum/peak stress at failure) and toughness related to

elastic energy for failure (area under the stress-strain curve till the maximum/

peak stress at failure) of cement-stabilized clayey silty soils increases signifi-

cantly by inclusion of PP and processed cellulose fibres, thus indicating a high

resistance to tensile cracking (Khattak and Alrashidi 2006).

9. The beam/flexural tests indicate that the improvement in tensile strain at crack

initiation of fine-grained soils (kaolin-sand mixes) is found to depend upon soil

type, moulding water content, fibre content and aspect ratio. For soil beams

without any fibres, the tensile strain at crack initiation is found to be in the

range of 0.83–1.09%. For soil beams reinforced with discrete, randomly dis-

tributed PP fibres, it was found to be in the range of 0.97–2.27%. This indicates

the significant influence of fibres in enhancing the tensile strength-strain char-

acteristics of moist-compacted soil beams (Viswanadham et al. 2010).

10. The ratio of UCS to split tensile strength (STS) for PP fibre (7 mm long) –

poorly graded sand (PP) – fat clay mixtures varies between 3.2- and 3.5-fold.

For 1.0% fibre inclusion, the ratio of UCS to STS is found to be minimum for

2.5% sand content. On the other hand, for 0.25% fibre inclusion, the ratio of

UCS to STS is observed as the maximum for 7.5 and 10% sand content (Yilmaz

2009).

11. The Brazilian tensile strength test results indicate that the maximum improve-

ment in tensile strength of cement-stabilized fibre-reinforced fly ash occurs by

addition of about 1% PP fibre, 60 mm in length, for both soaked and unsoaked

conditions (Chore and Vaidya 2015).


Chapter Summary

1. Improvement of engineering properties of soil due to the random inclusion of

discrete fibres is a function of a large number of parameters/factors relating soil

and fibre characteristics; fibre concentration and orientation; the presence of

admixtures, if any; method of mixing; type and amount of compaction; and test

and field conditions.

2. Contribution of fibres is more effective after a certain level of shear strain

depending on the types of fibre and soil. The inclusion of fibres increases the

peak strength (shear, compressive, tensile, etc.) of sandy soil by a mechanism

that involves the partial suppression of dilation, resulting in an increase in

effective confining stress and a consequent increase in shear strength.

3. Inclusion of fibres in soil reduces the post-peak strength loss, increases the axial

strain at failure and changes the stress-strain behaviour from strain softening to

strain hardening. Stiffness of soil can decrease at low strains by inclusion of

fibres.

4. Inclusion of fibres in a cement-stabilized soil improves its overall engineering

behaviour by increasing tensile and compressive strengths, peak angle of

internal friction angle, cohesion intercept, ductility (energy absorption capac-

ity), toughness (resistance to impact) and resistance to cyclic loading (fatigue).

Fibres do not prevent the formation of cracks, but they control directly the

crack propagation and improve the post-cracking properties.

5. UCS of fibre-reinforced clay soil is highly dependent on dry unit weight, water

content and fibre content. At a constant dry unit weight and water content, an

increase in the fibre content results in a significant increase in the UCS value.

An increase in the dry unit weight of reinforced clay specimens prepared at a

constant water content and fibre content results in a significant increase inUCS.An increase in water content of reinforced specimens at the same dry unit

weight and fibre content results in a reduction in the UCS.6. Failure occurs by frictional slipping of fibres for confining stresses up to a

threshold value referred to as the critical confining stress. For stresses greater

than the critical confining stress, the failure takes place by the rupture of the

fibres, that is, the failure is governed by the tensile strength of the fibres.

7. In general, increasing the fibre content leads to a reduction in the maximum dry

unit weight and an increase in optimum water content.

8. Seepage velocity of water through a fibre-reinforced soil mass is governed by

fibre content, fibre length and hydraulic gradient. An increase in fibre content

causes a decrease in seepage velocity and an increase in piping resistance of soil.

9. Clayey soils mixed with fibres show significantly lower swelling pressure and

swell potential in comparison with the same clayey soils without fibres.

10. Inclusion of fibres improves the CBR of the soil. The CBR value increases

significantly with increasing fibre content up to a specific value (say, around

0.75–1%) and remains more or less constant thereafter.

11. Addition of fibres to soil significantly improves its load-carrying capacity. For a

given load-bearing pressure, the settlement of unreinforced soil is more than


that of the reinforced soil, and the settlement reduces with an increase in fibre

content. The ultimate load-bearing capacity of the fibre-reinforced soil

increases with an increase in fibre content up to a specific value.

12. Tensile strength of soil increases significantly as a result of fibre inclusion. For

the same amount of fibres present in the reinforced soil, shorter and better

dispersed fibres contribute more to the tensile strength.

13. Inclusion of natural and glass fibres has a significant effect on the dynamic

response of sand, namely, shear modulus and damping ratio, which increase

approximately linearly with an increasing amount of fibres up to a specific

value of fibre content.

14. Improvement contributed by the presence of fibres is highly anisotropic

because of preferred sub-horizontal fibre orientations in compacted condition.

15. In clayey soils, the use of elevated moisture/water content, called the optimum

mixing moisture/water content (OMMC), may be required to produce effective

fibre-soil mixing.

16. Though the basic characteristics of fibre-reinforced soils have been studied and

reported by several researchers, the findings vary to some extent depending on

the variations in the parameters, but some observations also appear to be

contradictory. However, the present knowledge of fibre-reinforced soils pro-

vides the basic understanding of several factors to be analysed in detail while

working for any specific field application of fibre-reinforced soils.


(Select the most appropriate answer to the multiple-choice questions from Q 3.1 to

Q 3.5.)

3.1. Within the practical ranges of fibre content, in general, the shear strength of

fibre-reinforced soil

(a) Increases with increase in the fibre content, but decreases with an increase

in the fibre aspect ratio

(b) Decreases with increase in the fibre content, but increases with an increase

in the fibre aspect ratio

(c) Increases with increase in both the fibre content and the fibre aspect ratio

(d) Decreases with increase in both the fibre content and the fibre aspect ratio

3.2. Inclusion of PP fibres in sand generally increases its

(a) Strength and stiffness

(b) Strength and ductility

(c) Stiffness and ductility

(d) Strength, stiffness and ductility


3.3. An increase in the dry unit weight of fibre-reinforced clay specimens prepared

at a constant water content and fibre content causes the unconfined compres-

sive strength to

(a) Decrease significantly

(b) Decrease slightly

(c) Increase significantly

(d) Increase slightly

3.4. The optimum fibre content for achieving the maximum crack reduction and

maximum dry unit weight of clayey soil, while maintaining the acceptable

hydraulic conductivity, is typically between

(a) 0.4–0.5%

(b) 0.5–1%

(c) 1–2%

(d) 2–4%

3.5. In general, the CBR value of a reinforced soil continue to

(a) Increase with fibre content, but decrease with aspect ratio

(b) Decrease with fibre content, but increase with aspect ratio

(c) Decrease with both fibre content and aspect ratio

(d) Increase with both fibre content and aspect ratio

3.6. List the factors/parameters which govern the engineering behaviour of fibre-

reinforced soil.

3.7. Enumerate the fibre characteristics that may affect the engineering behaviour

of fibre-reinforced soils.

3.8. Illustrate with neat sketches the effect of increasing fibre content and fibre

length on the following properties of fibre-reinforced soil:

(a) Shear strength

(b) Unconfined compressive strength

(c) Permeability

(d) Compressibility

(e) California bearing ratio

(f) Load-bearing capacity

(g) Tensile strength

3.9. Define the following terms:

(a) Shear stress improvement factor at failure

(b) Deviator stress improvement factor at failure

(c) Deviator stress ratio at failure

(d) Unconfined compressive strength improvement factor

(e) Peak load ratio

(f) CBR improvement factor

(g) Bearing capacity ratio


3.10. Explain the interaction mechanisms between fibre and soil particles with the

help of a neat sketch.

3.11. Using the data presented in Table 3.4, plot the variation of deviator stress at

failure with fibre content for fibre aspect ratio of 100, considering cell

pressures of 40, 70, 100 and 140 kPa. Discuss the effect of increase of fibre

content on deviator stress. Is the variation linear?

3.12. Consider the following values of the deviator stress at failure:

For unreinforced soil, (σ1� σ3)fU¼ 1.65 MPa

For fibre-reinforced, (σ1� σ3)fR¼ 0.78 MPa

Determine the deviator stress improvement factor at failure. What does this

indicate?

3.13. What is brittleness index? Explain its importance.

3.14. Compare the engineering characteristics of fibre-reinforced sand and

cement-stabilized fibre-reinforced sand.

3.15. What is the difference between strength and stiffness of a soil? How does

inclusion of fibres affect them?

3.16. Define the critical confining stress, and explain its significance.

3.17. Draw the typical principal stress envelop for the fibre-reinforced sand as

obtained from triaxial compression tests. Comment on the shape of the

envelope.

3.18. Why do fibre-reinforced soils have a lower unit weight than unreinforced

soils? Explain briefly.

3.19. Do you see any significant difference between strength values of soil

reinforced with natural and polymeric fibres? Explain briefly.

3.20. Differentiate between the stress-strain curves for unreinforced and fibre-

reinforced soils as obtained from unconfined compression tests.

3.21. Discuss the effect of fibres on failure pattern of fibre-reinforced soils when

loaded.

3.22. How do the compaction parameters of fibre-reinforced soil differ from those

for unreinforced soil?

3.23. Explain the effect of fibre inclusion on the critical hydraulic gradient and

piping resistance of soil.

3.24. Can fibre inclusion control the swelling potential of expansive soils? Justify

your answer.

3.25. Polypropylene fibres are available in the following two forms: (i) L¼ 15

mm, D¼ 0.05 mm and (ii) L¼ 25 mm, D¼ 0.1 mm, where L and D are

length and diameter of fibres, respectively. If a sandy soil is to be reinforced,

which form of the fibres should be recommended for strength improvement?

Justify your answer.

3.26. What is the effect of fibre inclusion on the CBR value of high compress-

ibility clayey soil?

3.27. What is deformability index? Explain its importance.


3.28. Consider the following values of ultimate bearing capacity obtained from a

plate load tests on unreinforced and fibre-reinforced soils:

For unreinforced soil, quU¼ 85 kPa

For fibre-reinforced soil, quR¼ 115 kPa

Determine the ultimate bearing capacity ratio and ultimate bearing capacity

improvement factor. What does this factor indicate?

3.29. Discuss the failure modes as observed in the plate load tests on cement-

stabilized fibre-reinforced sand bed.

3.30. Draw the typical load-settlement curves for unreinforced and fibre-reinforced

sands as obtained from plate load tests. Discuss the effect of fibres.

3.31. How does fibre inclusion affect the dynamic response of dune sand?

3.32. What is the effect of fibre inclusion on the tensile strength of cement-

stabilized fibre-reinforced sand?

3.33. How can you investigate the stress-strain behaviour of fibre-reinforced soil at

large strains? Name the test which may be suitable for this study?


3.1 (c)

3.2 (b)

3.3 (c)

3.4 (a)

3.5 (d)

3.12 112%, 112% increase in deviator stress

3.26 length ¼ 15 mm, diameter ¼ 0.05 mm

3.29 1.35, 35%

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Chapter 4

Soil Reinforcing Mechanisms and Models

4.1 Introduction

In Chap. 3, you have learnt that when the fibres are included within a soil mass, they

cause changes in the properties (e.g. permeability, compressibility, shear strength,

etc.) of soil. The presence of fibres in a soil mass improves its stability, increases its

load-carrying capacity and reduces its deformation (i.e. settlement and lateral

movement). The effect of fibre inclusions on strength and stiffness behaviours of

soil is explained through the role of fibres as a reinforcement element. This chapter

presents the basic mechanisms and models of soil reinforcement, focusing on the

random distribution of fibres within the soil mass, resulting in randomly distributedfibre-reinforced soil (RDFRS), or simply the fibre-reinforced soil (FRS), as

explained in the previous chapters.

4.2 Basic Soil Reinforcing Mechanisms

If the reinforced soil is considered a homogeneous material, but with anisotropic

characteristics, the Mohr-Coulomb failure criterion can be applied to explain the

basic mechanism of reinforced soil. Consider a simplified situation, shown in

Figs. 4.1a, b, where two cylindrical specimens of a cohesionless soil are subjected

to the same triaxial loading with the minor principal stress (confining stress) σ3 andthe major principal stress σ1. The first soil specimen is not reinforced, but the

second one is reinforced with fibres. Figure 4.1c shows a magnified view of the

reinforced soil element, as indicated in Fig. 4.1b, with a horizontal fibre. Because of

skin friction and/or adhesion between the fibre and the soil, the fibre applies a

confining stress σR (¼Δσ3, increase in the minor principal stress) on the soil, and in

this process, the fibre gets stretched with mobilization of a tensile force Tf as shown



111

http://dx.doi.org/10.1007/978-981-10-3063-5_3

in Fig. 4.1c. Note that the tensile force Tf and hence the confining stress σR will varywith orientation of the fibre within the soil mass.

Assume that the Mohr-Coulomb failure criterion has been attained in the

unreinforced soil specimen. For this case, the stress state within the soil mass can

be represented, in the normal stress (σ) and shear stress (τ) space, by a Mohr circle

‘a’ as shown in Fig. 4.2, which is tangent to the Mohr-Coulomb failure envelope lUfor the unreinforced soil. If the reinforced soil specimen is subjected to the same

stress state, then due to skin friction and/or adhesion bonding between both

constituents, the lateral deformation/strain of the specimen reduces. The lateral

deformation of the reinforced soil specimen is generally greater than that of the

reinforcement but smaller than the lateral deformation of the unreinforced soil

specimen. This means that in the case of perfect friction and/or adhesion bonding

between reinforcement and soil, the reinforcement is extended, resulting in a

mobilized tensile force Tf, and the soil is compressed by additional compressive

lateral stress as the reinforcement restraint σR (¼Δσ3), introduced into the soil mass

in the direction of the reinforcement as shown in Fig. 4.1c. The stress state in soil

represented by the Mohr circle ‘b’ in Fig. 4.2 is no more tangent to the failure

envelope lU, and hence the reinforced soil specimen is able to sustain greater

stresses than those in the case of unreinforced soil.

Consider that the reinforced soil specimen, shown in Fig. 4.1b, is expanding

horizontally due to a decrease in applied horizontal stress σ3 with a constant verticalstress σ1, and assume that the failure occurs by rupture of the reinforcement, that is,

the lateral restraint σR is limited to a maximum value σRCmax depending on the

strength of the reinforcement. This state of stress is represented by the Mohr circle

‘c’ in Fig. 4.2. The strength increase can be characterized by a constant cohesion

intercept cR as an apparent cohesion, introduced due to reinforcement (Schlosser

and Vidal 1969). The results obtained from both the triaxial compression tests and

the direct shear tests on sand specimens reinforced with tensile inclusions have

Soil

Fibre

)( 31 σσ >

Rσ3σ

)( 31 σσ >

3σ

3R σσ Δ=

fTfT

(a) (b) (c)

Fig. 4.1 Basic soil reinforcing mechanism: (a) unreinforced cylindrical soil specimen; (b) fibre-reinforced cylindrical soil specimen; (c) magnified view of a reinforced soil element, as indicated

in (b)

112 4 Soil Reinforcing Mechanisms and Models

shown that the apparent cohesion of the reinforced soil is a function of the

orientation of the inclusions with respect to the direction of the maximum extension

in the soil (Long et al. 1972; Schlosser and Long 1974; Jewell 1980; Gray and

Al-Refeai 1986). Thus, the strength envelope for a reinforced cohesionless soil for

reinforcement rupture condition can be interpreted in terms of the Mohr-Coulomb

failure envelope lRC for the homogeneous cohesive soil as shown in Fig. 4.2.

For Mohr circle ‘a’, the principal stresses σ1 and σ3 are related as

σ1 ¼ σ3tan2 45∘ þ ϕ=2ð Þ ð4:1Þ

where ϕ is the angle of shearing resistance (or angle of internal friction) of the

unreinforced soil.

For Mohr circle ‘c’, representing the stress state of the reinforced soil at failure,

the principal stresses σ1 and σ3min are related as

σ1 ¼ σ3mintan2 45∘ þ ϕ=2ð Þ þ 2cR tan 45∘ þ ϕ=2ð Þ ð4:2Þ

Since σ3min¼ σ3� σRCmax, as seen in Fig. 4.2, Eq. (4.2) becomes

σ1 ¼ σ3 � σRCmaxð Þtan 2 45∘ þ ϕ=2ð Þ þ 2cR tan 45∘ þ ϕ=2ð Þ ð4:3Þ

Combining Eqs. (4.1) and (4.3) leads to

cR ¼ σRCmax tan 45∘ þ ϕ=2ð Þ2

¼ σRCmax

ffiffiffiffiffiffiKp

p2

¼ σRCmax

2ffiffiffiffiffiffiKa

p ð4:4Þ

Reinforcement rupture failure

Reinforcement slippage failure lRClRF

lU

c

Normal stress, s

Shea

r stre

ss, t

ab

f

gdecR

s1maxs30 min s3 mins30 s3 s3R

sRF Δs10 sRC max sR

s10 s10 max

fRf

f

s1

Δs1

Fig. 4.2 Basic mechanism of fibre-reinforced soil: Mohr circles for reinforced and unreinforced

cases

4.2 Basic Soil Reinforcing Mechanisms 113

where

Ka ¼ tan 2 45∘ � ϕ=2ð Þ ð4:5Þ

and

Kp ¼ tan 2 45∘ þ ϕ=2ð Þ ð4:6Þ

Note that Ka and Kp are the Rankine’s coefficients of active and passive lateral

earth pressures, respectively. Also note that the anisotropic cohesion is produced in

the direction of reinforcement orientation, and this concept is based on the labora-

tory shear strength studies on reinforced soil specimens.

You may now consider that the reinforced soil specimen shown in Fig. 4.1b is

expanding horizontally due to a decrease in applied horizontal stress σ3¼ σ30 with aconstant vertical stress σ1¼ σ10, as represented by the Mohr circle ‘d’, and assume

that the failure occurs by a slippage between the reinforcement and the soil, that is,

the lateral restraint σR is limited to σRF, which is proportional to σ10. Therefore,

σRF ¼ σ10F ð4:7Þ

where F is a friction factor that depends on the cohesionless soil-reinforcement

interface characteristics. This concept is based on the Yang’s experimental results

(Yang 1972) as presented by Hausmann and Vagneron (1977). The failure state of

stress is represented by the Mohr circle ‘e’ in Fig. 4.2. The strength increase can becharacterized by an increased friction angle ϕR. Thus, the strength envelope for a

reinforced cohesionless soil for the reinforcement slippage condition can be

interpreted in terms of the Mohr-Coulomb failure envelope lRF for the homoge-

neous cohesionless soil as shown in Fig. 4.2.

For Mohr circle ‘d’, the principal stresses σ10 and σ30 are related as

σ10 ¼ σ30tan2 45∘ þ ϕ=2ð Þ ð4:8Þ

Substituting Eq. (4.5) into Eq. (4.8) yields

σ10 ¼ σ30Ka

ð4:9Þ

For Mohr circle ‘e’, the principal stresses σ10 and σ30min are related as

σ10 ¼ σ30mintan2 45∘ þ ϕR=2ð Þ ð4:10Þ

Since σ30min¼ σ30� σRF, as seen in Fig. 4.2, Eq. (4.10) becomes

σ10 ¼ σ30 � σRFð Þtan 2 45∘ þ ϕR=2ð Þ ð4:11Þ


Substituting Eq. (4.7) into Eq. (4.11) yields

σ10 ¼ σ30 � σ10Fð Þtan 2 45∘ þ ϕR=2ð Þ ð4:12Þ

Combining Eqs. (3.8) and (3.12) leads to

1 ¼ Ka � Fð Þ 1þ sinϕR

1� sinϕR

� �

or

sinϕR ¼ 1þ F� Ka

1� Fþ Ka

ð4:13Þ

You may now consider that the reinforced soil specimen shown in Fig. 4.1b is

expanding horizontally due to an increase in applied σ1 with a constant σ3, andassume that the failure occurs by rupture of the reinforcement or reinforcement

slippage. These failure states of stress are represented by the Mohr circles ‘f’ and ‘g’in Fig. 4.2, respectively. Note that the reinforcement increases the compressive

strength of the soil by Δσ1 or Δσ10 depending on the type of failure mode of the

reinforced soil as indicated in the figure.

A different concept of the influence of reinforcement on the behaviour of

reinforced soil mass was described by Basset and Last (1978). It is suggested that

an introduction of reinforcement modifies the dilatancy characteristics of soil with a

possible rotation of principal strain directions. This concept is based on the fact that

if the dilation of the soil is restricted, the shear strength mobilized will be higher

than for the case of no restriction. The presence of reinforcement in soil imposes a

condition of restricted dilatancy. It also predetermines the principal incremental

strain directions and rotates them relative to the unreinforced case, thereby resulting

in a redistribution of stresses.

Note that the behaviour of soil reinforced with extensible reinforcements, such

as geosynthetic reinforcements, does not fall entirely within the concepts as

described here. For the details of reinforcing mechanisms of geosynthetic-

reinforced soils, the readers may refer to the books by Shukla (2002, 2012, 2016)

and Shukla and Yin (2006).

Example 4.1For a reinforced sand, consider the following:

Angle of shearing resistance of unreinforced sand, ϕ¼ 33∘

Friction factor, F¼ 0.1

Determine the angle of shearing resistance of the reinforced sand.

SolutionFrom Eq. (4.5), the Rankine’s active earth pressure coefficient,

4.2 Basic Soil Reinforcing Mechanisms 115

Ka ¼ tan 2 45∘ � ϕ=2ð Þ ¼ tan 2 45∘ � 33∘=2ð Þ ¼ 0:295

From Eq. (4.13),

sinϕR ¼ 1þ F� Ka

1� Fþ Ka

¼ 1þ 0:1� 0:295

1� 0:1þ 0:295¼ 0:674

Therefore, angle of shearing resistance of the reinforced sand is

ϕR ¼ sin�1 0:674ð Þ ¼ 42:4∘

4.3 Basic Models of Fibre-Reinforced Soils

Based on the experimental studies, it has been established that the strength and

deformation characteristics of the fibre-reinforced soils are governed by the soil and

fibre characteristics as well as by confinement and stress level. The states of stress

and strain in fibre-reinforced soils during its deformation and failure are complex.

However, for engineering applications, it is possible to explain the mechanism of

fibre reinforcements in soils, especially the contribution of fibres to the shear

strength increase, and hence the behaviour of fibre-reinforced soils, by mathemat-

ical approaches/models. The finite element analyses considering appropriate con-

stitutive relationships can be carried out to investigate the behaviour of fibre-

reinforced soils. The commercial software can be used for such analyses without

developing the complete codes. In the past, the researchers have attempted to

present some simplified models, which are based on different approaches, such as

force-equilibrium/mechanistic approach, energy dissipation approach, statistical

approach and the approach of superposition of the effects of soil and fibres. Some

of these models are presented here.

4.3.1 Waldron Model

The root-reinforced soil mass can be considered a composite material in which the

roots of relatively a high tensile strength are embedded in a matrix of lower tensile

strength. Waldron (1977) proposed a simple force-equilibrium model to estimate

the increase in strength of soil reinforced with non-rigid plant roots, taking into

account the tensile force developed in the root reinforcement and considering the

same in the Mohr-Coulomb’s equation in its modified form as


SR ¼ Sþ ΔS ¼ cþ σ tanϕþ ΔS ð4:14Þ

where SR is the shear strength of reinforced soil, S is the shear strength of

unreinforced soil, ΔS is the shear strength increase caused by plant root reinforce-

ment, σ is the total normal confining stress applied on the shear/failure plane and

c and ϕ are shear strength parameters, namely, the cohesion intercept and angle of

shearing resistance, respectively, of the unreinforced soil. This model is based on

the observations made when the root-permeated cylindrical soil specimens of

250-mm diameter were brought to zero matric potential and sheared in a large

direct shear device. The roots are assumed to be vertical, flexible, elastic, of

uniform diameter and extending an equal distance on either side of the horizontal

shear plane. Only the partial mobilization of fibre tensile strength is considered

depending upon the amount of fibre elongation during the shear. This model does

not place any constraint on the distribution or location of the reinforcing fibres.

Note that the plant roots increase the soil shear strength both directly by

mechanical reinforcing and indirectly through water removal by transpiration.

4.3.2 Gray and Ohashi (GO) Model

The concept of the Waldron model was extended by Gray and Ohashi (1983) to

describe the deformation and the failure mechanism of fibre-reinforced cohesion-

less soil and to estimate the contribution of fibre reinforcement to increasing the

shear strength of soil. The model consists of a long, elastic fibre, extending an equal

length over either side of a potential shear plane in sand (Fig. 4.3). The fibre may be

oriented initially perpendicular to the shear plane or at some arbitrary angle i withthe horizontal. Shearing causes the fibre to distort, thereby mobilizing the tensile

resistance in the fibre. The tensile force in the fibre can be divided into components

normal and tangential to the shear plane. The normal component increases the

confining stress on the failure plane, thereby mobilizing additional shear resistance

in the sand, whereas the tangential component directly resists the shear. The fibre is

assumed to be thin enough that it offers little if any resistance to shear displacement

from the bending stiffness. If many fibres are present, their cross-sectional areas are

computed, and the total fibre concentration is expressed in terms of the fibre arearatio, Ar, defined by Eq. (2.7) as reproduced below:

Ar ¼ Af

Að4:15Þ

where Af is the total cross-sectional area of fibres in a plane (e.g. shear/failure plane)

within the reinforced soil mass and A is the total area of the plane (e.g. shear/failure

plane) within the reinforced soil mass, which includes the soil particles, fibres and

voids.

4.3 Basic Models of Fibre-Reinforced Soils 117

The shear strength increase ΔS (¼SR� S, SR and S are shear strengths of

reinforced soil and unreinforced soil, respectively) from the fibre reinforcement

in sand can be estimated from the following expressions:

ΔS ¼ σR sin θ þ cos θ tanϕð Þ ð4:16Þ

for fibres oriented initially perpendicular to the shear plane (Fig. 4.3a), and

ΔS ¼ σR sin 90� � ψ

� �þ cos 90� � ψ

� �tanϕ

� �¼ σR cos ψ þ sinψ tanϕð Þ ð4:17Þ

for fibres oriented initially at some arbitrary angle i with the horizontal (Fig. 4.3b),

with

ψ ¼ tan �1 z

xþ x0

� �¼ tan �1 1

k þ cot i

� �ð4:18Þ

where σR is the mobilized tensile strength of fibres per unit area of fibre-reinforced

granular soil, which mainly comes from the fibres; ϕ is the angle of internal friction

of unreinforced soil; θ is the angle of shear distortion; x is the horizontal shear

displacement; z is the thickness of shear zone; i is the initial orientation angle of the

Shear zone

xIntact fibrea

b

Deformed fibres

zq

ft

fsfs

ft

90°=i

Shear zone

Intact fibreDeformed fibres

ft

ft

fsfs

z

90°<i

y

xx¢is

Normal confining stress, s

Fig. 4.3 Model for flexible,

elastic fibre reinforcement,

extending across the shear

zone of thickness z:(a) i¼ 90∘; (b) i< 90∘

(Adapted from Gray and

Ohashi 1983; Shukla et al.

2009)


fibre with respect to shear surface, x0 ¼ z cot i; and k(¼x/z) is the shear distortion

ratio.

The mobilized tensile strength of fibres per unit area of soil (σR) can be estimated

as

σR ¼ Arσf ¼ Af

A

� �σf ð4:19Þ

where σf is the maximum tensile stress developed in the fibre at the shear plane,

which depends upon a number of parameters and the test variables. The fibres must

be long enough and frictional enough to avoid the pullout; conversely, the confining

stress must be high enough so that the pullout forces do not exceed the skin friction

(i.e. interface shear forces) along the fibre. It is also necessary to assume some sort

of tensile stress distribution along the length of the fibre. Two likely or reasonable

possibilities are linear and parabolic distributions, with tensile stress a maximum at

the shear plane and decreasing to zero at the fibre ends. The resulting tensile stresses

at the shear plane for these two distributions are given by the following expressions

(Waldron 1977):

σf ¼ 4EfτfD

� �1=2

z sec θ � 1ð Þ½ �1=2 ð4:20Þ

for the linear distribution, and

σf ¼ 8Efτf3D

� �1=2

z sec θ � 1ð Þ½ �1=2 ð4:21Þ

for the parabolic distribution, where Ef is the modulus or longitudinal stiffness of

the fibre, τf is the skin friction stress along the fibre and D is the diameter of fibre.

The GO model has been found to predict correctly the influence of various

parameters (fibre area ratio, fibre length, fibre modulus, initial fibre orientation and

sand relative density), which govern the shear strength of fibre-reinforced soil as

observed in the direct shear tests conducted by Gray and Ohashi (1983). For

example, in the direct shear tests, the maximum shear strength increase, both

theoretically and experimentally, was observed for the fibres placed at an angle of

60�with the shear plane, that is, in the direction of major principal strain.

Note that a variation of Waldron force-equilibrium model was proposed by

Jewell and Worth (1987) by placing the stiff reinforcement symmetrically, that is,

extended equally about the central horizontal/shear plane in direct shear tests. The

force in the reinforcement acting across the shear plane is resolved into components

normal and tangential to the shear plane. These two components of the reinforce-

ment force are considered to improve the shearing strength of the soil by directly

reducing the shear force acting on the soil and by increasing the available frictional

shearing resistance in the soil. The expression for shear strength increase presented


by Jewell and Worth (1987) is similar to those proposed by Waldron (1977) and

Gray and Ohashi (1983) (Eqs. (4.16) and (4.17)).

4.3.3 Maher and Gray (MG) Model

Based on the observations made in triaxial compression tests and statistical analysis

of strength of randomly distributed fibre-reinforced sand, Maher and Gray (1990)

proposed a model for predicting its strength behaviour when subjected to static

loads. The model considers the following assumptions:

1. The reinforcing fibres have a constant length and diameter, and they do not offer

any resistance to bending.

2. The smaller portion of a fibre length on either side of the failure plane is

uniformly distributed between zero and half of the fibre length.

3. The fibres have an equal probability of making all possible angles with any

arbitrarily chosen fixed axis, that is, the failure surfaces in triaxial compression

tests on granular soil are planer and oriented in the same manner as predicted by

the Mohr-Coulomb failure criterion.

4. The fibres in the soil mass and, equivalently, their points of intersection with any

failure plane are randomly distributed following a Poisson-type distribution.

5. For the sand-fibre composites, the principal stress envelope, that is, the plot of

major principal stress at failure (σ1f) versus the minor principal stress (confining

stress) (σ3), is either curved linear or bilinear, with the transition or the break

occurring at a threshold confining stress, referred to as the critical confining stress,σ3crit (Fig. 4.4). For σ3< σ3crit, the fibres slip during deformation, and for

σ3> σ3crit, they stretch or yield. Assuming a Mohr-Coulomb failure criterion, the

reinforced soil envelope is parallel to that of unreinforced soil above the critical

confining stress.

The increase in shear strength from the fibre reinforcement can be estimated

from the following expressions:

ΔS ¼ Ns

πD2

4

� �2arσ3av tan δð Þ sin θ þ cos θ tanϕð Þη ð4:22Þ

for 0< σ3av< σ3crit, and

ΔS ¼ Ns

πD2

4

� �2arσ3crit tan δð Þ sin θ þ cos θ tanϕð Þη ð4:23Þ

for σ3av> σ3crit,where σ3av is average confining stress in the triaxial chamber, Ns is

the average number of fibres intersecting a unit area of the shear plane, ar is theaspect ratio of fibres, δ is the fibre skin friction angle and η is an empirical


coefficient depending on the soil characteristics (median/average particle size D50,

particle sphericity Ss and coefficient of uniformity CU) and the fibre parameters

(aspect ratio and skin friction). The value of σ3crit can be determined empirically

from the experimental measurements, thus depending on the soil characteristics and

the fibre properties.

Note that in Fig. 4.4, for σ3< σ3crit, the stress envelope for fibre-reinforced sand

is either linear or nonlinear depending on the types of sand and reinforcement.

The MG model has predicted the increase in the strength of the fibre-reinforced

soil reasonably well when compared to the experimental values. However, the

width of shear zone z, which significantly affects the increase in strength

(Shewbridge and Sitar 1989, 1990), has not been determined for the reinforced

soil, as it is also not determined in the Waldron and GO models. Also, the average

expected orientation of fibres is statistically predicted to be perpendicular to the

plane of shear failure. It is difficult to determine experimentally the exact orienta-

tion of fibres. Note that the model proposed by Jewell and Worth (1987) for stiff

reinforcements also does not pay an attention to the formation of shear zone, which

significantly affects the increase in shear strength of reinforced soil.

4.3.4 Ranjan, Vasan and Charan (RVC) Model

Ranjan et al. (1996) proposed a model based on the statistical/regression analysis of

the data obtained from more than 500 triaxial compression tests on the randomly

distributed discrete fibre-reinforced soil. This model quantifies the effect of fibre

Unreinforced sand

Fibre-reinforced sandReinforcement slip

Reinforcementstretch

Critical confining stress (3 crits )

Confining stress, 3s

Maj

or p

rinci

pal s

tress

at f

ailu

re, s

1f

Fig. 4.4 Effect of the fibre inclusion in sand on its principal stress envelope obtained from the

triaxial compression tests (Adapted from Maher and Gray 1990; Shukla and Sivakugan 2010)


properties, soil characteristics and confining stress on the shear strength of the

reinforced soil. The mathematical expression of the model is as follows:

σ1f ¼ f pf ; ar; f∗; f ; σ3ð Þ ð4:24Þ

where σ1f is the major principal stress at failure of fibre-reinforced soil (i.e. shear

strength of fibre-reinforced soil), pf is the fibre content, ar is the fibre aspect ratio, f∗

is the surface friction coefficient, f is the coefficient of friction and σ3 is the

confining stress. The expressions for f and f∗ are given below:

f ¼ c

σþ tanϕ ð4:25Þ

and

f∗ ¼ caa

σþ tanϕi ð4:26Þ

where σ is the total normal confining stress applied on the shear/failure plane; c andϕ are shear strength parameters, namely, the cohesion intercept and angle of

shearing resistance, respectively, of the unreinforced soil; ca is the adhesion inter-

cept; and ϕi is the angle of skin friction as determined from fibre pullout tests. A

value of 100 kPa for σ may be adopted for calculating f and f∗ using Eqs. (4.25) and

(4.26), respectively. The regression analysis has considered the following

assumptions:

1. The response parameter σ1f is a random quantity with normal distribution law,

which is followed by most distributions in nature.

2. The variance of σ1f does not depend on its absolute value. That is, the variances

are homogeneous.

3. The values of independent factors (i.e. pf , ar , f∗ , f , σ3, etc.) are not random

quantities.

The failure envelope of fibre-reinforced soil is curvilinear with a transition at

certain confining stress, called the critical confining stress σ3crit (see Fig. 4.4).For σ3� σ3crit,

σ1f ¼ 12:3 pfð Þ0:4 arð Þ0:28 f∗ð Þ0:27 fð Þ1:1 σ3ð Þ0:68 ð4:27Þ

For σ3� σ3crit,

σ1f ¼ 8:78 pfð Þ0:35 arð Þ0:26 f∗ð Þ0:06 fð Þ0:84 σ3ð Þ0:73 ð4:28Þ

Note that the values of coefficient of determination R2 in Eqs. (4.27) and (4.28)

are found to be greater than 0.90, which indicates a good fit of the data used. The

value of σ3crit is observed to decrease with an increase in aspect ratio ar of fibres, asindicated in Fig. 4.5; however, it is relatively unaffected by the amount of fibre


content pf as indicated in Fig. 4.5, where the data points of both pf¼ 1% and

pf¼ 2% have been represented by the same curve.

4.3.5 Zornberg Model

Zornberg (2002) presented a discrete model for predicting the shear strength of

fibre-reinforced soil based on the independent properties of fibres and soil (e.g. fibre

content, fibre aspect ratio and shear strength of unreinforced soil). The fibres are

assumed to contribute to the shear strength increase by mobilizing tensile stress

along the plane of shear (Fig. 4.6). Therefore, the shear strength SR of fibre-

reinforced soil has the following two components: the shear strength S of soil

matrix and the fibre-induced distributed tensile force per unit area σR. Thus

SR ¼ Sþ ασR ¼ cþ σ tanϕþ ασR ð4:29Þ

where σ is the total normal confining stress applied on the shear/failure plane, c andϕ are the cohesion intercept and angle of shearing of the unreinforced soil and α is

an empirical coefficient that accounts for the orientation of fibres. For the case of

randomly oriented fibres, α equals 1. For any preferred orientation, α should be

selected suitably between 0 and 1.

Under low confining stresses, when the failure is governed by pullout of the

fibres, the fibre-induced distributed tensile force can be estimated as

σRP ¼ arpvf ci, ccþ ci,ϕσ tanϕ� � ð4:30Þ

Aspect ratio, ra

050 75 100 125

50

100

150

Crit

ical

con

finin

g st

ress

, s3c

rit (k

Pa)

%21f -=p

Fig. 4.5 Effect of aspect

ratio ar on critical confining

stress σ3crit for plastic fibre-reinforced soil (Adapted

from Ranjan et al. 1996)


where ar is the fibre aspect ratio, pvf is the volumetric fibre content and σ is the

average normal stress acting on the fibres. The parameters ci , c and ci ,ϕ are

interaction coefficients defined as

ci, c ¼ a

cð4:31Þ

ci,ϕ ¼ tan δ

tanϕð4:32Þ

where a is the adhesion between the soil and the fibre and δ is the interface frictionangle.

Note that the fibre-induced distributed tension is a function of fibre content pvf,fibre aspect ratio ar and interaction coefficients ci , c and ci ,ϕ if the failure is

governed by the fibre pullout.

Using Eq. (4.30) with σR¼ σRP, Eq. (4.29) is expressed to obtain the shear

strength of fibre-reinforced soil when the failure is governed by fibre pullout as

SRP ¼ cþ σ tanϕþ ασR ¼ cþ σ tanϕþ α arpvf ci, ccþ ci,ϕσ tanϕ� ��

or

SRP ¼ cRP þ tanϕð ÞRPσ ð4:33Þ

where

cRP ¼ 1þ αarpvfci, cð Þc ð4:34Þ

and

S

Failure/shear surface

Fibre

Tensile force in fibre

Rs

Fig. 4.6 A fibre-reinforced

soil mass with fibres

intersecting the failure/

shear surface


tanϕð ÞRP ¼ 1þ αarpvfci,ϕ� �

tanϕ ð4:35Þ

When failure is governed by the yielding of the fibres, that is, the fibre tensile

breakage, the fibre-induced distributed tensile force is a function of fibre content pvfand tensile strength σf , ult of individual fibres and can be estimated as

σRt ¼ pvfσf, ult ð4:36Þ

Using Eq. (4.36) with σR¼ σRt, Eq. (4.29) is expressed to obtain the shear

strength of fibre-reinforced soil when the failure is governed by the tensile breakage

of the fibres as

SRt ¼ cRt þ tanϕð ÞRtσ ð4:37Þ

where

cRt ¼ cþ αpvfσf, ult ð4:38Þ

and

tanϕð ÞRt ¼ tanϕ ð4:39Þ

Note that Zornberg (2002) presented the discrete model for the design of fibre-

reinforced soil slopes. The fibres as discrete elements are considered to contribute

to stability by mobilizing tensile stresses along the shear/failure surface, as shown

in Fig. 4.6. At the critical normal stress,

σRP ¼ σRt ð4:40Þ

Using Eqs. (4.30) and (4.36) with σ¼ σcrit, the expression for σcrit is obtained as

σcrit ¼ σf, ult � arci, c c

arci,ϕ tanϕð4:41Þ

Thus, the critical normal stress σcrit at which the governing mode of fibre failure

changes from fibre pullout to fibre breakage is a function of tensile strength of

fibres, soil shear strength and aspect ratio, but is independent of the fibre content.

Note that the pullout resistance of a fibre of length L, if required to be

quantified, should be estimated over the shortest side of the two portions of the

fibre intercepted by the failure surface. The length of the shortest portion of the fibre

intercepted by the failure surface varies from zero to L/2. Statistically, the averageembedment length of randomly distributed fibres, Le , av, can be defined analyticallyas Le , av¼ L/4 (Zornberg 2002).


4.3.6 Shukla, Sivakugan and Singh (SSS) Model

Shukla et al. (2010) developed a simple analytical model for predicting the shear

strength behaviour of fibre-reinforced granular soils under high confining stresses,

where it can be assumed that pullout of fibres does not take place. The derivation of

the analytical expression is presented below.

The shear strength of the unreinforced dry granular soil is given as (Lambe and

Whitman 1979; Shukla 2014)

S ¼ σ tanϕ ð4:42Þ

where σ is the total normal confining stress applied on the shear plane and ϕ is the

angle of shearing resistance (or the angle of internal friction) of the granular soil.

Most of the experimental studies have shown that if fibres are added to the

granular soil, there is an increase in shear strength of the soil. Assuming no pullout

under high confining stresses, the increase in shear strength ΔS for the systemati-

cally distributed/oriented fibre-reinforced granular soil as shown in Fig. 4.3b can be

expressed by Eq. (4.17) (Gray and Ohashi 1983).

Addition of Eqs. (4.17) and (4.42) gives the shear strength SR of the systemat-

ically oriented fibre-reinforced granular soil as

SR ¼ Sþ ΔS ¼¼ σR cosψ þ σ þ σR sinψð Þ tanϕ ð4:43Þ

Assuming that the unreinforced granular soil does not carry any tensile stress,

the mobilized tensile strength per unit area of reinforced granular soil (σR) can be

estimated using Eq. (4.19).

Note that the fibres are assumed long enough and frictional enough to resist

pullout; conversely the confining stress must be high enough to ensure that pullout

forces do not exceed skin friction (i.e. interface shear forces) along the fibre. It is

also necessary to assume some form of tensile stress distribution along the length of

the fibre. Assuming a constant shear stress distribution along the length of the fibre,

an expression for the tensile stress σf developed in the fibre can be derived as

σf � π

4D2

¼ L

2� πD

� �σið Þ

� �tanϕi sin i

or

σf ¼ 2σiL

D

� �tanϕi sin i ¼ 2σiar tanϕi sin i ð4:44Þ

where σi is normal stress on the fibre inclined to the horizontal at an angle i; L and

D are the length and the diameter of the fibres, respectively; ar(¼L/D) is the aspectratio of the fibres; and ϕi is the fibre-soil interface friction angle. The expression for

σi is given as (Jewell and Wroth 1987)


σi ¼ 1� sinϕ sin ϕ� 2ið Þcos 2ϕ

� �σ ð4:45Þ

The term sini is included in Eq. (4.44) as an empirical scaling constant to account

for the fibre orientation. From Eq. (4.44), for i¼ 0∘, σf¼ 0, which indicates that if

fibres are not stretched and are oriented parallel to the shear plane, they will have no

tension, because shear mobilization does not take place in the absence of anchoring

of the ends of fibres. Here σi¼ σ. For i¼ 90∘, sini¼ 1, and σf 6¼ 0. In fact, when

fibres are normal to the shear plane, one can expect that the maximum shear

mobilization takes place due to full anchoring of the ends of the fibres. Substituting

Eq. (4.45) into Eq. (4.44) gives

σf ¼ 2σ ar tanϕi sin i1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

� �ð4:46Þ

Substituting Eqs. (4.19) and (4.46) into Eq. (4.43) yields

SR ¼ cR þ σRS tanϕ ð4:47Þ

where

cR ¼ σ 2Arar tanϕi sin i cosψ1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

�� ð4:48Þ

and

σRS ¼ σ 1þ 2Arar tanϕi sin i sinψ1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

�� ð4:49Þ

Comparing Eqs. (4.42) and (4.47), it can be seen that the effect of reinforcing

with systematically oriented fibres is to introduce an apparent cohesion cR to the

granular soil and to increase the normal confining stress on the shear plane from σ toσRS, thereby increasing the shear strength of granular soil. The parameters cR and

σRS are the apparent cohesion and improved confining normal stress in the fibre-

reinforced granular soil. Note that both cR and σRS are functions of area ratio Ar,

aspect ratio ar, skin friction δ, normal confining stress σ and distortion angle ψ .The shear strength improvement of the granular soil due to inclusion of fibres

can be described in terms of a dimensionless ratio, called the shear strength ratio(SSR), as defined below:

SSR ¼ SRS

ð4:50Þ


Substituting Eqs. (4.42) and (4.47) into Eq.(4.50) gives

SSR ¼ 1þ 2Arar1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

� �sinψ þ cosψ

tanϕ

� �tanϕi sin i ð4:51Þ

In a very thin element of the randomly distributed fibre-reinforced soil (Fig. 4.7),

if Af1, Af2 Af3,..., Afn are the areas of cross section of the fibres at a shear plane, Asoil

is the area of the soil section, including voids at the shear plane, and ΔL is the

thickness of the element measured perpendicular to the shear plane, the area ratio

Ar(¼Af/A) of the randomly distributed fibre-reinforced soil at the shear plane can be

expressed as

Ar ¼ Af

A¼ Af1 þ Af2 þ Af3 þ :::::þ Afnð Þ

Af1 þ Af2 þ Af3 þ :::::þ Afnð Þ þ Asoil

� ΔLΔL

¼ Vsf

Vsf þ Vsoil

ð4:52Þ

where Vsf is the volume of fibre solids and Vsoil is the volume of soil, including

voids, in the element of the fibre-reinforced soil.

Eq. (4.52) can be rearranged as

Vsf

Vsoil

¼Af

A

� �1� Af

A

� � ¼ Ar

1� Ar

ð4:53Þ

The ratio of weight of the fibre solids Wsf to the weight of the soil solids Wss,

called the fibre content pf, in an element of reinforced soil (Fig. 4.7), can be

expressed as

pf ¼Wsf

Wss

¼ VsfGfγwVssGγw

¼ VsfGf 1þ esð ÞVsoilG

¼ Gf 1þ esð ÞGm

Ar

1� Ar

� �ð4:54Þ

or

Ar ¼pf

GGf 1þesð Þh i

1þ pfG

Gf 1þesð Þh i ð4:55Þ

where Gf is the specific gravity of fibre solids, G is specific gravity of soil solids and

es is the void ratio of soil.

Substituting Eq. (4.55) into Eqs. (4.48), (4.49) and (4.51) provides

cRσ

¼ 2ar tanϕi sin i cosψpf

GGf 1þesð Þn o

1þ pfG

Gf 1þesð Þn o

24

35 1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

� �ð4:56Þ


σRS � σ

σ¼ 2ar tanϕi sin i sinψ

pfG

Gf 1þesð Þn o

1þ pfG

Gf 1þesð Þn o

24

35 1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

� �

ð4:57Þ

and

SSR ¼ 1þ 2ar tanϕi sin i sinψ þ cosψ

tanϕ

� �1� sinϕ sin ϕ� 2ið Þ

cos 2ϕ

� �

�pf

G

Gf 1þ esð Þ �

1þ pfG

Gf 1þ esð Þ �

2664

3775

ð4:58Þ

Considering a uniform strain distribution, the stress-strain relationship for the

fibre can be expressed as

σf ¼ Ef

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixþ x0ð Þ2 þ z2

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix02 þ z2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffix02 þ z2

q264

375 ¼ Ef

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiz2 þ z2cot 2ψ

pffiffiffiffiffiffiffiffiz2þp

z2cot 2i� 1

!¼

¼ Ef

sin i

sinψ� 1

� �ð4:59Þ

where Ef is the Young’s modulus of elasticity of fibres in extension.

Comparing Eq. (4.46) with Eq. (4.59) yields

Afn

Af7

Af5Af4

Af2

Af3

Af6

Af1

DL

Fig. 4.7 An element of

fibre-reinforced granular

soil of thicknessΔL


sinψ ¼ sin i

1þ 2ar tanϕi sin iσEf

1� sinϕ sin ϕ�2ið Þ

cos 2ϕ

h i ð4:60Þ

and

cosψ

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos 2iþ 4ar tanϕi sin i

σ

Ef


cos 2ϕ

� �1þ ar tanϕi sin i

σ

Ef


cos 2ϕ

�� s

1þ 2ar tanϕi sin iσ

Ef


cos 2ϕ

� �

ð4:61Þ

Substituting values of sinψ and cosψ from Eqs. (4.60) and (4.61), respectively,

into Eq. (4.56), (4.57) and (4.58) gives the following:

cRσ

¼ 2β1β2pf

GGf 1þesð Þn o

1þ pfG

Gf 1þesð Þn o

24

35

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos 2iþ 4β1β2

σEf

1þ β1β2

σEf

h ir

1þ 2β1β2σEf

2664

3775 ð4:62Þ

σRS � σ

σ¼ 2β1β2

pfG

Gf 1þesð Þn o

1þ pfG

Gf 1þesð Þn o

24

35 sin i

1þ 2β1β2σEf

24

35 ð4:63Þ

and

SSR ¼ SRS

¼ 1þ 2β1β2

pfG

Gf 1þ esð Þ �

1þ pfG

Gf 1þ esð Þ �

2664

3775�

sin i

1þ 2β1β2σ

Ef

� �2664 þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffifficos 2iþ 4β1β2

σ

Ef

� �1þ β1β2

σ

Ef

� �� s

1þ 2β1β2σ

Ef

� �� tanϕ

377775

ð4:64Þ

with

β1 ¼ ar tanϕi sin i ð4:65aÞ

and


β2 ¼1� sinϕ sin ϕ� 2ið Þ

cos 2ϕð4:65bÞ

Eq. (4.62) provides an expression for ratio of apparent cohesion to normal

confining stress on the shear plane; Eq. (4.63) gives an expression for the ratio of

increase in normal confining stress to the normal confining stress; and Eq. (4.64)

defines an expression for SSR, which is the ratio of shear strength of reinforced soilto that of unreinforced soil.

Note that Eq. (4.64) is quite useful in predicting the variation of SSR with fibre

content pf, aspect ratio L/D, ratio of confining stress to modulus of fibres σ/Ef,

specific gravity of fibre solids Gf and initial orientation of fibres with respect to

shear plane i for any specific sets of parameters in their practical ranges. The effects

of pf, ar and i on SSR for specific sets of parameters are shown in Figs. 4.8, 4.9, and

4.10, respectively.

In Fig. 4.10, you may note that as i increases, SSR also increases with its

maximum value for i ¼ 74�for the set of parameters taken. A similar trend has

also been reported by Gray and Ohashi (1983) in their experimental study. They

reported that an initial orientation of 60�with the shear plane is the optimum

orientation for maximum increase in shear strength. This direction is approximately

the principal tensile strain direction in a dense sand as reported by Jewell (1980).

For the randomly distributed fibre-reinforced soil, i can vary from 0�to 180

�. For

the purpose of calculating the increase in shear stress caused by inclusion of

randomly distributed fibres in a granular soil, i ¼ 90�can be taken for the

orientation of fibres in Eq. (4.64) for simplicity in analysis. Though the observations

from the analytical model matches with the experimental observations in trends of

variation of parameters, it is felt that large-scale tests will be suitable for comparing

the observations with the results from this model.

It is worth noting the following:

1. The inclusion of fibres in the granular soil induces cohesion, may be called the

apparent cohesion, as well as an increase in the normal stress on the shear failure

plane, which are proportional to the fibre content and the aspect ratio, implying

that the increase in shear strength is also proportional to the fibre content and the

aspect ratio.

2. The increase in shear strength of the granular soil due to presence of fibres is

significantly contributed by the apparent cohesion, and the contribution to the

shear strength from the increase in normal confining stress is limited.

3. As the initial orientation of fibres with respect to shear plane (i) increases, theSSR also increases to a maximum value for a specific value of i depending on thevalues of other governing parameters.


Example 4.2Determine the shear strength ratio (SSR) for the following three cases:

(a) Fibre content, pf¼ 0%

(b) Soil-fibre interface friction angle, δ¼ 0∘

(c) All fibres are oriented parallel to the shear plane, i¼ 0∘

Explain the physical significance of SSR value obtained for each case.

Solution(a) For pf¼ 0%, from Eq. (4.64),

SSR ¼ SRS

¼ 1

This result is well expected when there are no fibres present in the soil.

(b) For δ¼ 0∘, from Eq. (2.65a), β1¼ 0, and hence from Eq. (4.64),

SSR ¼ SRS

¼ 1

This suggests that if fibres are not having frictional resistance in contact with

soil particles, their inclusion in soil will not be useful. In this situation, there is no

Fibre content, (%)fp

f = 36° G = 2.66 se = 0.7

if = 24°fG = 1.38 i = 90°

f/ Es = 0.5

Shea

r stre

ngth

ratio

, SSR

ra = 125 100 75 50 25

0 0.5 1 1.5 2 2.5 31

1.5

2

2.5

3

Fig. 4.8 Effect of fibre content pf on the shear strength ratio SSR of fibre-reinforced soil (Adapted

from Shukla et al. 2010)


Aspect ratio, ra

Shea

r stre

ngth

ratio

, SSR

f = 36° G = 2.66 se = 0.7

if = 24°fG = 1.38 i = 90°

f/ Es = 0.5

3(%)f =p 2 1

0 10 20 30 40 50 60 70 801

1.5

2

2.5

3

Fig. 4.9 Effect of aspect ratio ar on the shear strength ratio SSR of fibre-reinforced soil (Adapted

from Shukla et al. 2010)

Initial inclination of fibre to the shear plane, i

Shea

r stre

ngth

ratio

, SSR

f = 36° G = 2.66 se = 0.7

if = 24°fG = 1.38 ra = 75

f/ Es = 0.5 fp = 1%

0 10 20 30 40 50 60 70 80 901

1.5

2

2.5

3

3.5

Fig. 4.10 Effect of initial inclination of fibre to the shear plane i on the shear strength ratio SSR of

fibre-reinforced soil (Adapted from Shukla et al. 2010)


shear stress acting along the surface of the fibres, and therefore the fibres remain

unstretched.

(c) For i¼ 0∘, from Eq. (2.65a), β1¼ 0, and hence from Eq. (4.64),

SSR ¼ SRS

¼ 1

This suggests that if all the fibres are oriented parallel to the shear plane, there

will be no increase in shear strength.

4.4 Other Models and Numerical Studies

The behaviour of fibre-reinforced soils has been investigated numerically by

several researchers by developing their own analysis and numerical programmes/

codes or by using the commercial finite element/difference software. Some

researchers have also attempted to present constitutive models based on certain

assumptions for solving boundary-value problems with fibre-reinforced soils as a

numerical analysis. The non-uniformity of fibre orientations and anisotropy have

also been described in terms of a specific fibre orientation distribution function,

resulting in an anisotropic constitutive model (Diambra et al. 2007).

Michalowski and Zhao (1996) proposed a model using the energy-based homog-

enization (averaging) technique to quantify the effect of fibre inclusion on the shear

strength behaviour of granular soil. The model considers that the fibres contribute to

the strength of the fibre-reinforced soil only if they are subjected to tension, whereas

their influence in the compressive regime is neglected due to possible buckling and

kinking. This model is basically a mathematical description of a failure criterion for

fibre-reinforced granular soil in terms of in-plane variants q (radius of the Mohr

circle representing the state of stress, that is, shear stress, σ01 � σ

03

� �=2) and p (mean

of the maximum and minimum principal stresses, that is, mean principal stress,

σ01 þ σ

03

� �=2) in a macroscopic/global stress space as stated below:

q

pvfσ0¼ p

pvfσ0sinϕþ 1

3N 1� 1

4arpvf

cotϕi

ppvfσ0

24

35 ð4:66Þ

with

N ¼ 1

πcosϕþ 1

2þ ϕ

π

� �sinϕ ð4:67Þ

where pvf is the volumetric fibre content, σ0 is the yield stress of the fibre material,

ar is the aspect ratio of fibre, ϕ is the angle of internal friction of the granular matrix

and ϕi is the soil-fibre interface friction angle.


Failure of a single fibre in a deforming fibre-reinforced soil can occur due to fibre

slip or tensile rupture. When a fibre fails in the tensile rupture mode, the slip also

occurs at both fibre ends up to the distance s, as given below:

s ¼ D

4

σ0σn tanϕi

ð4:68Þ

where σn is the stress normal to the fibre surface and D is the diameter of the fibre.

Note that the slip also occurs at both fibre ends up to the distance s because the

tensile strength of the fibre material cannot be mobilized throughout the entire fibre

length. A pure slip failure mode may occur if the length of fibres L becomes less

than 2s, or when the aspect ratio

ar <1

2

σ0σn tanϕi

ð4:69Þ

A comparison of the Michalowski and Zhao’s model with the experimental

results demonstrates the adequacy of the model. When the pure slip occurs, the

failure criterion takes the following form:

q

pvfσ0¼ p

pvfσ0sinϕþ 1

3Npvfar tanϕi

� �ð4:70Þ

When fibres are not present, both Eqs. (4.66) and (4.70) reduce to the standard

Mohr-Coulomb failure criterion for granular material as

q ¼ p sinϕ ð4:71Þ

Figure 4.11 shows the results from Eqs. (4.66) and (4.70) in the q� p plane withdifferent curves presenting the failure criteria for fibre-reinforced soil with fibres of

various aspect ratios. As indicated in Eq. (4.70), the slip mode is described by a

linear variation for a constant ϕ, whereas in the tensile rupture mode, the shear

strength is not proportional to the mean stress p (Eq. (4.66)). The following points

regarding Michalowski and Zhao’s model are worth mentioning:

1. Five parameters (volumetric fibre concentration pvf, fibre aspect ratio ar, fibreyield stress σ0, internal friction angle of soil ϕ and soil-fibre interface friction

angle ϕi) are needed to theoretically predict the failure stress. For a pure fibre

slip failure mode, the failure criterion is independent of the fibre yield stress σ0.2. The transition from one failure mode to another is continuous and smooth

(continuous derivative).

3. The model is applicable for low value of pvf, say less than 10%, so that

interaction between fibres may be neglected. The length L of fibres needs to be

at least one order of magnitude larger than the granular soil particle diameter,

and the fibre diameter D needs to be at least of the same order as the size of

granular soil particle.

4.4 Other Models and Numerical Studies 135

4. The model is limited to isotropic mixtures, that is, the fibre-reinforced soil with

isotropic distribution of fibre orientations.

5. The model indicates that the fibres may be an effective way for soil reinforce-

ment when mixtures with a larger fibre content or larger aspect ratios are used.

The stiffness of the soil prior to failure is affected by the addition of fibres, and,

for flexible fibres, it drops down with respect to the stiffness of the granular soil.

The contribution of fibres to the strength of fibre-reinforced soils is very much

dependent on the distribution and orientation of the fibres within the soil mass. The

fibres in the direction of largest extension contribute most to the strength of the

reinforced soil, whereas the fibres under compression have an adverse effect on the

stiffness, and they do not produce an increase in the strength. Michalowski and

Cermak (2002) presented a failure criterion for fibre-reinforced sand with an

anisotropic distribution of fibre orientation, considering contribution of a single

fibre to the work dissipation during failure of the reinforced sand and integrating

this dissipation over all fibres in a reinforced sand element. This failure criterion

can be applied directly in methods for solving stability problems for fibre-

reinforced sand.

Ding and Hargrove (2006) established a nonlinear stress-strain relationship of

the equivalent homogeneous and isotropic material for flexible fibre-reinforced soil,

assuming there is no slip at soil-fibre interface and breakage of fibres. The devel-

opment of the stress-strain relation is based on the consideration of energy in soil

and energy in fibres. This constitutive model relates the shear modulus of the fibre-

reinforced soil with the fibre content, distribution, geometrical features and soil-

fibre interaction.

Babu et al. (2008a) presented the results of a numerical analysis of a cylindrical

sand specimen (diameter ¼ 38 mm, height ¼ 76 mm) reinforced with the coir fibres.

0vfspp

0 0.5 1 1.5 20

0.5

1

1.5

0vfspq

40r =a

120r =a

¥=ra

Unreinforced granular soil

Reinforced granular soil

Fig. 4.11 Theoretical

failure criterion for fibre-

reinforced granular soil

(Note: pvf¼ 0.02, ϕ¼ 35∘

and ϕi¼ 20∘) (Adapted

fromMichalowski and Zhao

1996)


They used the finite difference code, Fast LagrangianAnalysis of Continua (FLAC3D),

for the investigation. The results show that the presence of random fibre reinforcement

in sand makes the stress concentration more diffused and restricts the shear band

formation. The stress-strain response of the reinforced sand is governed by the pullout

resistance of the fibres as the maximum mobilized tensile force (2.1 to 3.6 N) under

different confining pressures is generally less than the tensile strength of the fibres

(5 N). The mobilized tensile force in a fibre within sand increases with increasing

confining pressure. No definite peak in the stress-strain diagram is observed in

numerical analysis as the peaks are noticed in experimental stress-strain diagrams.

Based on the standard triaxial compression test data, Babu and Vasudevan

(2008a) presented statistical models using regression for predicting the major

principal stress at failure σ1fR, cohesion intercept cR, angle of internal friction ϕR

and initial stiffness EiR of soil reinforced with coir fibres, as given below:

σ1fR kPað Þ ¼ 159:1þ 3:96σ3 � 0:0083σ23 � 2959Dþ4866:5D2 � 37:01pf þ 17:35p2f þ 58:8L� 1:69L2

þ2:69σ3Dþ 548:61Dpf þ 6:21Lpf � 0:016Lσ3

ð4:72Þ

cR kPað Þ ¼ 76:5þ 156:4D� 102:1D2 þ 126:1pf � 39:3p2f þ 20:2Dpf ð4:73Þ

ϕR degreesð Þ ¼ 23:1� 78:55Dþ 191:1D2 þ 7:03pf þ 2:38p2f � 15:02Dpf ð4:74Þ

EiR kPað Þ ¼ 8992:2þ 64:94σ3 � 0:14σ23 � 94612Dþ186594D2 � 1744:9pf þ 1167:8p2f þ 1765:1L�52:1L2 þ 33:3σ3Dþ 11707:7Dpf þ 129:77Lpf�0:47Lσ3

ð4:75Þ

where σ3 is the confining pressure (kPa), D is the diameter of fibres (mm), L is the

length of fibres (mm) and pf fibre content (%). The value of R2 for the above-

presented four equations are 0.95, 0.98, 0.99 and 0.89, respectively, which are close

to unity, and hence these equations can be considered satisfactory for the coir fibre-

reinforced soils.

Babu and Vasudevan (2008b) have also presented regression equations for

quantifying the seepage velocity and the piping resistance of coir fibre-reinforced

soil considering hydraulic gradient, fibre contents and fibre lengths. In another

study, Babu et al. (2008b) developed equations similar to Eqs. (4.72), (4.73) and

(4.74) for coir fibre-reinforced black cotton soil and also the following expression

for its compression index CcR with R2 of 0.98:

CcR ¼ 0:506� 0:129pf þ 0:01p2f ð4:76Þ


Example 4.3A black cotton soil is reinforced with coir fibres. The fibre content is 0.2%. What is

the effect of fibre inclusion on the compression index of soil?

SolutionFrom Eq. (4.76), the compression index of unreinforced black cotton soil

( pf¼ 0%) is

CcU ¼ 0:506� 0:129pf þ 0:01p2f ¼ 0:506� 0:129ð Þ 0ð Þ þ 0:01ð Þ 0ð Þ2 ¼ 0:506

From Eq. (4.76), the compression index of coir fibre-reinforced black cotton soil

( pf¼ 0.2%) is

CcR ¼ 0:506� 0:129pf þ 0:01p2f ¼ 0:506� 0:129ð Þ 0:2ð Þ þ 0:01ð Þ 0:2ð Þ2¼ 0:4806

Thus, the compression index of black cotton soil decreases from 0.506 to 0.4806

due to inclusion of fibres. The percentage decrease is

ΔCc

CcU

� 100 ¼ CcU � CcR

CcU

� 100 ¼ 0:506� 0:4806

0:506� 100 ¼ 5:02%

Diambra et al. (2010) proposed a modelling approach for coupling the effects of

fibres with the stress-strain behaviour of unreinforced soil, based on the basic rule

of mixtures, and presented a constitutive model for the fibre-reinforced sand mass,

as stated below:

Δσ ¼ Δσ0 þ pvfΔσf ¼ Mm½ �Δεþ pvf Mf½ �Δε ð4:77Þ

where Δσ is the total stress increase, Δσ0is the stress increase in sand particles, pvf

is the volumetric fibre content,Δσf is the stress increase in fibres,Mm is the stiffness

matrix for the sand, Mf is the stiffness matrix for the fibres and Δε is the strain

increase in sand particles and fibres, caused by stress increase Δσ. Equation (4.77)

considers that no sliding occurs between sand particles and fibres, and the fibres

only act elastically in tension; thus the strains are equal in sand particles and fibres.

This assumption is used in developing the stiffness matrix for the fibres. The sand

stiffness matrix can be developed using the Mohr-Coulomb model or any other

suitable model. In this constitutive model, any distribution of fibre orientations can

be accounted for, and importance of considering the fibre orientation relative to the

strain conditions can be explained. The model has been calibrated against the

results of drained triaxial compression and extension tests, and a good agreement

has been observed.

Note that the test results obtained from the direct shear tests conducted by

Shewbridge and Sitar (1989) using a large direct shear device show that the shear

zones tend to be wider in reinforced soil composites than in soil alone. The width of

the shear zones increases with increasing stiffness of the composite due to any

combination of increased reinforcement concentration (measured by area ratio),


stiffness and reinforcement-soil bond strength. Volume changes associated with the

development of the shear zones are not spatially homogeneous. A linear relation-

ship between reinforcement concentration and increased strength is not observed,

and thus this observation contradicts the earlier observations. The actual deforma-

tion pattern of the reinforcement-soil composite can be described by a smooth

asymptotic curve in the following form (Shewbridge and Sitar 1989, 1990):

Y ¼ δ

21� e�k Xj j� � ð4:78Þ

where X and Y are the axes or coordinate directions perpendicular and parallel to the

direction of shear, respectively, with the origin at the centre of the shear zone

(Fig. 4.12); δ is the externally applied shear displacement; and k is a deformation

decay constant, which is basically a curve-fitting parameter describing the shape of

the curve. The value of k can be determined from the maps of deformed soil

specimens subjected to a known total shear displacement δ. The constant

k provides a measure of the thickness of the shear zone and of the distribution

and magnitude of shear strains within it. For the specimens with relatively thin

shear zones, which contain large shear strains, the value of k is large. For the

specimens with large shear zones containing small shear strains, the value of k is

small. The value of k decreases as the fibre area ratio increases, that is, the shear

zone width increases with an increase in reinforcement concentration. The value of

k also decreases with an increase in reinforcement stiffness and soil-reinforcement

interface bond strength. Thus, the shear zone width, as measured by the deforma-

tion decay constant k, increases with increasing reinforcement concentration, rein-

forcement stiffness and soil-reinforcement bond strength.

The deformation pattern, defined by Eq. (4.78), differs significantly from the

simple shear deformation pattern assumed in the models, described in Sec. 4.3. In

fact, there is still a need of further study based on large-scale field tests to

investigate more realistic picture of shear zone development and width of shear

zone in the fibre-reinforced soil because the shear zone significantly governs the

strength and deformation of the reinforced soil.

Chapter Summary

1. If the failure occurs by rupture of the reinforcement, the strength increase can

be characterized by a constant cohesion intercept cR as an apparent cohesion,

introduced due to reinforcement. If the failure occurs by a slippage between the

reinforcement and the soil, the strength increase can be characterized by an

increased friction angle ϕR. In general, a fibre-reinforced soil typically shows

the bilinear strength behaviour.

2. If the failure is characterized by pullout of individual fibres, the fibre-induced

distributed tension increases linearly with fibre content and fibre aspect ratio.

3. Simplified models of fibre-reinforced soil are based on different approaches,

such as force-equilibrium/mechanistic approach, energy dissipation approach,

statistical approach and the approach of superposition of the effects of soil and

fibres.


4. Waldron model and Gray and Ohashi (GO) model have correctly described the

characteristics of reinforced soil in direct shear, in which the failure/shear plane

is predetermined and the reinforcement is placed at certain angle with the

failure plane. Hence these models are applicable only for oriented inclusions.

5. Maher and Gray (MG) model; Shukla, Sivakugan and Singh (SSS) model; and

statistical models predict reasonably well the increase in strength of randomly

distributed fibre-reinforced soils as these models are based on the triaxial

compression tests.

6. The SSS model provides a more generalized analytical expression for estimat-

ing the shear strength increase as a result of fibre inclusion within the soil mass.

7. Width of shear zone should be considered for developing the models for more

realistic estimation of improvement in the strength of fibre-reinforced soils.

8. Available statistical models provide the empirical expressions based on limited

characteristics of soils and fibres, and hence they should not be used as the

generalized expressions for estimating the engineering properties of fibre-

reinforced soils.

9. Constitutive models can be developed using the basic rule of mixtures as

required for any specific application. Equation (4.77) is an example of such a

model, which considers that no sliding occurs between sand particles and

fibres, and the fibres only act elastically in tension; thus the strains are equal

in sand particles and fibres.

10. Behaviour of fibre-reinforced can be investigated numerically considering the

appropriate constitutive models. Non-uniformity of fibre orientations and

anisotropy can easily be considered in numerical models.

X

Y

Z

2/d

2/d

Deformed fibre

Fig. 4.12 Schematic geometry of deformed reinforcement in the coordinate space (Adapted from

Shewbridge and Sitar 1989, 1990)


Questions for Practice(Select the most appropriate answer to the multiple-choice questions from Q 4.1 to

Q 4.5.)

4.1. A fibre within a soil mass can apply confining stress by

(a) Skin friction

(b) Adhesion

(c) Both (a) and (b)

(d) Cohesion

4.2. Which of the following conditions may cause the fibres to slip during defor-

mation of the fibre-reinforced soil?

(a) σ3< σ3crit(b) σ3> σ3crit(c) σ3� σ3crit(d) None of the above

4.3. The effect of width of shear zone is not considered in

(a) Waldron model

(b) GO model

(c) MG model

(d) all of the above

4.4. Which of the following models is a statistical/regression model?

(a) Waldron model

(b) RVC model

(c) SSS model

(d) None of the above

4.5. Shear strength of the fibre-reinforced soil increases with

(a) Increasing fibre content and decreasing aspect ratio

(b) Decreasing fibre content and increasing aspect ratio

(c) Increasing both fibre content and aspect ratio

(d) Decreasing both fibre content and aspect ratio

4.6. Explain the basic reinforcing mechanism of fibre-reinforced soil.

4.7. What is critical confining stress? Explain its importance. Derive an expression

for the critical confining stress.

4.8. Under what conditions, the fibre reinforcement within the soil mass may slip or

rupture?

4.9. For a reinforced sand, consider the following:

Angle of shearing resistance of unreinforced sand, ϕ¼ 30∘

Friction factor, F¼ 0.15

Determine the angle of shearing resistance of the reinforced sand.


4.10. What are the assumptions of Maher and Gray model? Is this model of fibre-

reinforced soils based on observations made in triaxial compression tests? Is

this model applicable to all types of fibre-reinforced soils? Justify your answer.

4.11. What are the limitations of GO, MO and SSS models?

4.12. Can you use the available statistical models as the generalized models to

estimate the engineering properties of soils? Explain briefly.

4.13. List the parameters/factors considered in the SSS model. Derive the analyt-

ical expression for the shear strength ratio proposed by the SSS model of the

fibre-reinforced soil.

4.14. What is the key advantage of using the Zornberg model?

4.15. Explain the effect of aspect ratio on the critical confining stress.

4.16. Using the SSS model, discuss the effects of the following on the shear

strength of fibre-reinforced soil:

(a) Soil-fibre interface friction angle (δ)(b) Modulus of elasticity of fibres (Ef)

(c) Angle of shearing resistance of soil (ϕ)

4.17. What is physical meaning of having the shear strength ratio (SSR) of unity fora fibre-reinforced soil?

4.18. Derive the following relationship:

SSR ¼ 1þ cRσ

1

tanϕþ σRS � σ

σ

Show the variation of SSR, cR/σ and (σRS� σ)/σ with the fibre content pf fortypical values of soil and fibre parameters.

4.19. Explain the model of fibre-reinforced soil developed using the energy-based

homogenization technique. What are the key features of this model?

4.20. Explain the constitutive model for the fibre-reinforced soil mass developed

using the basic rule of mixtures. Is there any limitation of this model?

4.21. A black cotton soil is reinforced with coir fibres. The fibre content is 0.6%.

What is the effect of fibre inclusion on the compression index of soil?

4.22. Shear zones tend to be wider in fibre-reinforced soils than in soil alone. Is it

true? Justify your answer.


4.1 (c)

4.2 (a)

4.3 (d)

4.4 (b)

4.5 (c)

4.9 43.7�

4.21 14.58% decrease


References

Babu GLS, Vasudevan AK (2008a) Strength and stiffness response of coir fibre-reinforced tropical

soil. J Mat Civil Eng ASCE 20(9):571–577

Babu GLS, Vasudevan AK (2008b) Seepage velocity and piping resistance of coir fibre mixed

soils. J Irrig Drainage Eng ASCE 134(4):485–492

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Geotechnique 52(8):593–604


Chapter 5

Applications of Fibre-Reinforced Soil

5.1 Introduction

In the previous chapters, you studied about the basic characteristics of soils and

fibres, engineering behaviour of fibre-reinforced soils with or without other admix-

tures/additives (lime, cement, fly ash, etc.) and reinforcing mechanisms and

models. In most applications, the discrete fibres are simply added and mixed

randomly with soil or other similar materials (coal ashes, mine tailings, etc.), in

much the same way as lime, cement or other additives are used to stabilize and

improve the soil. However, some difficulties occur at the construction site in getting

a uniform mixture of soil and fibres. In the present-day construction practice, the

use of fibres is one of the cost-effective and environmentally friendly ground

improvement techniques. This chapter describes the possible field applications of

fibre-reinforced soils, focusing on presenting specific application/construction

guidelines.

5.2 Field Applications

Reinforcing the soil with discrete fibres is a ground improvement technique that has

not yet been fully utilized worldwide as this technique can be adopted in the

present-day engineering practice. This is probably because of unavailability of

standards and codes of practice, especially in developing countries. In comparison

with the systematically reinforced soils (i.e. soils with oriented reinforcements such

as the geosynthetic-reinforced soils), the randomly distributed/oriented fibre-

reinforced soils exhibit some advantages, as listed below:

1. Preparation of randomly distributed fibre-reinforced soils mimics the conven-

tional/traditional soil stabilization techniques, which uses the admixtures, such

as lime, cement, fly ash, etc. Hence, the field application or construction



145

procedure may be similar to that adopted for conventional soil stabilization

techniques.

2. Addition of fibre reinforcement in soil causes a significant improvement in

strength and stiffness, although a decrease in stiffness may take place as

reported in some studies.

3. Fibre-reinforced soil exhibits greater toughness and ductility and smaller losses

of post-peak strength as compared to soil alone.

4. Addition of fibres improves the permeability and compressibility/swelling

characteristics of soils.

5. Inclusion of fibres improves the load-carrying capacity of soils.

6. Addition of fibres significantly decreases the liquefaction potential of coarse

silts and fine sands.

7. Randomly distributed fibres with even orientations in all directions offer a

better isotropy in strength or other properties and limit the potential planes of

weakness that can develop parallel to the oriented reinforcement as included in

a systematically reinforced soil.

8. Before the failure takes place, because of greater extensibility characteristics of

fibre-reinforced soils, one can notice large strains/deformations in the fibre-

reinforced soil structures, and hence, suitable corrective measures may be taken

easily within the available time.

9. Fibre-reinforced soil can facilitate reinforcement of geoenvironmental barriers

where continuous/systematic reinforcements may result in a preferential path-

way for contaminant migrations.

10. Traditional planar reinforcements, such as geosynthetic reinforcements, when

used in slopes and other such irregular sections, need anchorage and excavation

into the slope, and there is a possibility of failures in addition to difficulty in

placement. The use of fibre reinforcement in these applications provides a

flexible solution.

11. Compared to the geosynthetic reinforcements, the fibre reinforcement can be

used in a limited space, especially for the stabilization of failed soil slopes.

12. The use of fibre reinforcement can result in economical solutions because fibres

have lower cost, and at some construction sites, they may be available freely as

geonaturals or waste materials, such as old tyres and plastics.

In view of several advantages and favourable characteristics, the fibre-reinforced

soils have a great potential for their applications in several areas, and they are now

recognized as a viable ground improvement technique. The key applications are the

following:

• Geotechnical applications: backfills behind the retaining structures; stabilization ofsoils beneath the footings and rafts; stabilization of failed soil slopes; construction

of embankments usingmarginal soils, and over weak soils, such as organic soft soil

deposits; lightweight fill materials; admixtures in fine sands and silts to increase the

resistance to liquefaction; and strengthening the granular piles and trenches

• Transportation applications: pavement subgrades, subbases and bases, espe-

cially for low-volume roads; drainage layers for roads, runways, playgrounds,

etc.; thermal insulator for limiting the frost penetration; and vibration damping

layers beneath railway tracks

146 5 Applications of Fibre-Reinforced Soil

• Hydraulic and geoenvironmental applications: admixtures in soil to control the

hydraulic conductivity; improving the soil resistance against water and wind

erosion; stabilization of thin soil veneers, landfill liners and final covers; admix-

tures for mitigating the formation of shrinkage/desiccation cracks in compacted

clays; controlling seepage and preventing the piping erosion in dams and other

water-retaining structures (river levees, contour bunds, canal diversion works,

check dams, etc.); leachate collection systems; and geotextile tube dewatering

applications

In reinforcement applications, the fibres are generally most effective when

oriented within the soil mass in the same direction as the tensile strains caused by

the applied loads. Hence, for any particular loading condition, the properties of

fibre-reinforced soil depend significantly on the orientation of fibres with respect to

the loading direction.

In the laboratory testing and the field/practical applications, the distribution of

fibres can usually be characterized by a preferred plane of fibre orientation

(Michalowski and Cermak 2002; Diambra et al. 2007). The orientation of fibres

depends on the following:

• Method of mixing of soil with fibres

• Specimen preparation method for tests

• Method of field placement

The laboratory test specimens are prepared in two stages, namely, mixing and

compaction. Water, as required, is added to the dry soil, and then mixed together

uniformly, followed by adding the fibres to the wet soil and mixing in order to have

the even distribution of fibres. The test specimens in the desired test mould are

prepared by one of the following techniques (Michalowski and Cermak 2002;

Diambra et al. 2010; Ibraim et al. 2012):

• Tamping technique: the soil-fibre mix is compacted in specific number of layers

by tamping with a rammer having a flat base.

• Vibration technique: the soil-fibre mix is densified by vibrating the test mould

filled with the soil-fibre mix on a vibration table.

Tamping and vibration techniques for preparing the fibre-reinforced soil speci-

mens in moist conditions lead to a preferred near-horizontal orientation of fibres.

Both techniques leave at least 80% of the fibres oriented between � 30� of

horizontal, and 97% of fibres have an orientation that lies within � 45� of the

horizontal plane. These techniques generally produce a soil fabric/structure that

resembles that of the rolled-compacted construction fills (Diambra et al. 2010;

Ibraim et al. 2012). Hence, inclusion of fibres in soil in the field application may

not result in isotropic properties of fibre-reinforced soil as generally considered, and

hence the use of some simplified isotropic models, as discussed in Chap. 4, may not

result in accurate predictions of the benefits attributed to fibres. For cases where the

predominant load is perpendicular to the preferred plane of fibre orientation, the

isotropic models, in general, under-predict the benefits from the fibres

(Michalowski and Cermak 2002).

5.2 Field Applications 147

http://dx.doi.org/10.1007/978-981-10-3063-5_4

As there are several factors affecting the engineering characteristics of fibre-

reinforced soil (see Sect. 3.2), the selection of fibres for any specific application

may not be an easy task. In spite of the fact that a significant amount of research has

been carried out worldwide, there is currently no scientific standard or code of

practice on fibre-reinforced soils and their applications. Typically, the selection

should consider the following (Hoover et al. 1982):

1. Survivability of the fibres within the soil mass with consideration of varying

nature of the soil-water system in regard to alkalinity, chemical composition,

temperature and environmental variations

2. Range of required mechanical properties of the fibres

3. Availability of fibres in length range required for the specific application

4. Potential inability to properly incorporate fibres into the soil to a random state of

orientation

5. Procurement cost of fibres

5.3 Analysis and Design Concepts

In Chap. 3, you learnt that the engineering behaviour of fibre-reinforced soil is

governed by a large number of factors/parameters. As described in Chap. 4,

attempts have been made to idealize the behaviour of fibre-reinforced soil, and

several models are now available to predict the specific engineering behaviour of

fibre-reinforced soil. However, it is difficult to suggest sound and rational design

methods for specific applications of fibre-reinforced soil as listed in the previous

section. Section 5.4 discusses the experience gained in some specific applications

and provides several application guidelines. Analysis and design concepts relating

the basic characteristics of fibre-reinforced soils for some field applications are

presented in this section. The actual design of the structure can be carried out in a

conventional way, considering the fibre-reinforced soil as one of the materials used

for the construction of a specific structure. For the final analysis and design of a

structure being constructed with fibre-reinforced soil, if possible, a suitable field

test should be carried out based on the detailed laboratory findings and observations

of the behaviour of fibre-reinforced soil.

Design of fibre-reinforced soil structures can be carried out by adopting one of

the following two approaches:

1. Composite approach: The fibre-reinforced soil structure is analysed in a tradi-

tional way, considering the engineering properties of fibre-reinforced soil as a

homogeneous material. It is based on the fact that inclusion of fibres contributes

to stability due to an increase in shear strength of the homogenized composite

reinforced soil mass, although the reinforcing fibres actually work in tension and

not in shear. The contribution of the fibres is typically quantified by an equiv-

alent cohesion intercept and angle of internal friction angle of the soil. Several

composite models, following different approaches (e.g. mechanical, statistical,

energy based, etc.) have been proposed as they are presented in Chap. 4.



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http://dx.doi.org/10.1007/978-981-10-3063-5_4

http://dx.doi.org/10.1007/978-981-10-3063-5_4

2. Discrete approach: The fibre-reinforced soil structure is analysed, considering

the contributions of soil and fibres separately (Zornberg 2002). Under shearing

caused by applied load, the fibre reinforcement contributes to the increase of

shear resistance of soil by mobilizing the tensile stresses within the fibres. The

analysis requires independent testing of soil and of fibres, but not of fibre-

reinforced soil. The results obtained are more realistic. Additionally the fibres

can be optimized in terms of their quality, content, aspect ratio, etc. for deliv-

ering the cost-effective designs. The fibre-induced distributed tension, σR, to be

used in this design approach to account for the tensile contribution of the fibres

in limit equilibrium analysis is taken as a minimum of σRP and σRt as they are

discussed in Chap. 4 for fibre pullout and fibre breakage cases, respectively.

In the current design practice, the fibre-reinforced soil structures are often

designed by discrete approach as the most geosynthetic-reinforced soil structures

are routinely designed based on working stress design method or limit state design

method. Note that the fibres, being flexible, may not remain straight and they may

get folded several times randomly within the specimen. It is difficult to consider this

situation exactly while analyzing the behaviour of fibre-reinforced soils by discrete

approach. Hence, some designers may prefer to design the fibre-reinforced soil by

adopting the composite approach, especially when the fibres of relatively higher

lengths are used.

In discrete approach, there is a need to properly consider the interfacial interac-

tion of fibres with soil particles through adhesion and/or friction. Studies may be

conducted to determine the ratio of adhesion to soil cohesion intercept and also for

the ratio of angle of skin friction to angle of internal friction of soil as these factors

are determined between soils and other construction materials (Potyondy 1961).

It is important to note that the long fibre-reinforced soils perform well when the

application of loading direction and magnitude is known. When the load and its

direction are not known, short, discrete, randomly distributed/oriented fibre-

reinforced soil may be preferred. The basic principles of reinforcement design are

the same for systematically reinforced soil and randomly distributed fibre-

reinforced soils, except that suitable reduction factors should be applied in the

case of randomly distributed fibre-reinforced soil. In the reinforced soil, only the

reinforcements aligned normal to the applied stress, carry any stress. In randomly

distributed fibre-reinforced soils, some fibres do not carry any stress at all, and this

should be accounted for by strength reduction factors, more commonly termed the

efficiency factors (Hoover et al. 1982).Achieving a uniform distribution of fibres at the construction site is generally a

difficult task. The poor distribution of fibres within the soil mass in the field

application may not result in the design property as expected based on the labora-

tory tests that may have a uniform distribution of fibres in test specimens. If the

distribution of fibres is not uniform, the laboratory property value should be

adjusted suitably by applying a factor of safety. In the case of strength property,

for considering the uncertainty induced by non-uniform fibre distribution, the

design strength of fibre-reinforced soil should be reduced to a value lower than

the laboratory strength.

5.3 Analysis and Design Concepts 149

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Michalowski (2008) presented the limit analysis of anisotropic fibre-reinfroced

soil, and considering the ellipsoidal distribution of fibres, defined a term as distri-bution ratio pr varying practically between 0 and 1. If the fibre-reinforced soil

behaves as an isotropic material, pr equals 1. The kinematic approach of limit

analysis was used to present the values of active earth pressure coefficient Ka and

the bearing capacity factor Nγ as given in Tables 5.1 and 5.2, respectively. The total

active earth pressure Pa against a rough vertical wall from the fibre-reinforced

cohesionless soil backfill (Fig. 5.1) and load-bearing capacity (average stress)

Table 5.1 Active earth

pressure coefficient Kafor a

rough vertical wall with fibre-

reinforced cohesionless soil

backfill

ϕ (degrees) δ (degrees) arpvf tanϕi pr Ka

30 15 0 – 0.301

0.2 1.0 0.271

0.5 0.260

0.2 0.245

0.4 1.0 0.242

0.5 0.221

0.2 0.193

0.6 1.0 0.215

0.5 0.184

0.2 0.145

35 15 0 – 0.248

0.2 1.0 0.218

0.5 0.207

0.2 0.192

0.4 1.0 0.189

0.5 0.168

0.2 0.141

0.6 1.0 0.162

0.5 0.131

0.2 0.094

40 15 0 – 0.201

0.2 1.0 0.171

0.5 0.160

0.2 0.146

0.4 1.0 0.142

0.5 0.121

0.2 0.096

0.6 1.0 0.115

0.5 0.085

0.2 0.048

After Michalowski (2008)

Note: ϕ is the angle of internal friction of soil, δ is the soil-wall

interface friction angle, ϕi is the fibre-soil interface friction angle,

ar is the aspect ratio of fibres. and pvf is the volumetric fibre

content


qa of a strip footing resting over fibre-reinforced cohesionless foundation soil

(Fig. 5.2) can be determined using the following expressions along with the values

of Ka and Nγ from Tables 5.1 and 5.2, respectively:

Pa ¼ 1

2KaγH

2 ð5:1Þ

Table 5.2 Bearing capacity

factor Nγ for fibre-reinforced

cohesionless foundation soil

ϕ(degrees) arpvf tanϕi pr Nγ

30 0 – 21.394

0.2 1.0 33.239

0.5 35.775

0.2 39.598

0.4 1.0 53.301

0.5 62.636

0.2 79.380

35 0 – 48.681

0.2 1.0 84.305

0.5 92.280

0.2 104.612

0.4 1.0 155.559

0.5 191.827

0.2 263.931

40 0 – 118.826

0.2 1.0 241.893

0.5 272.732

0.2 321.365

0.4 1.0 561.436

0.5 755.590

0.2 1207.296

After Michalowski (2008)

aP

d

Fibre-reinforced soil backfill

Retaining wall

FibresFig. 5.1 A retaining wall

with a vertical back face

supporting a fibre-

reinforced cohesionless soil

backfill


where γ is the total unit weight of fibre-reinforced backfill and H is the height of the

retaining wall.

qa ¼1

2γBNγ ð5:2Þ

where γ the total unit weight of fibre-reinforced foundation soil and B is the width of

the strip footing.

Note that Pa is inclined at an angle δ to the normal to the vertical back of the wall

because the analysis has considered a rough vertical wall.

The following points are worth mentioning:

1. Addition of fibres to the soil backfill reduces the active earth pressure coefficient

Ka and hence the total lateral earth pressure Pa on the wall.

2. The value of Pa decreases with an increase of the concentration of fibres in the

backfill, but it is also affected by the distribution of fibre orientation. The near-

horizontal-preferred orientations contribute significantly to the reduction of Pa.

3. As the internal friction of sand is increased with the addition of fibres, the

bearing capacity factor Nγ also increases. The anisotropic distribution of fibre

orientation contributes further to this increase; that is, the distribution of fibres

with the horizontal preferred plane benefits the bearing capacity more than the

isotropic distribution.

Example 5.1

For a fibre-reinforced sand backfill supported by an 8-m high retaining wall with a

vertical back face, consider the following:

Angle of internal friction of sand, ϕ¼ 30∘

Total unit weight of fibre-reinforced sand, γ¼ 15.61 kN/m3

Fibre-reinforced soil-wall interface friction angle, δ¼ 15∘

B

Fibre-reinforced foundation soil

Strip footing

Fibres

Load

Fig. 5.2 A strip footing

resting on a fibre-reinforced

cohesionless foundation soil


Fibre-soil interface friction angle,ϕi¼ 20∘

Fibre aspect ratio, ar¼ 75

Volumetric fibre content, pvf¼ 1%

Determine the total active earth pressure from the fibre-reinforced sand backfill

on the retaining wall, assuming the fibre-reinforced sand behaves as an isotropic

material.

Solution

As the fibre-reinforced sand behaves as an isotropic material, the distribution ratio,

pr ¼ 1

Using the given values,

arpvf tanϕi ¼ 75ð Þ 0:01ð Þ tan 20�ð Þ ¼ 0:273

From Table 5.1, the active earth pressure coefficient,

Ka ¼ 0:271� 0:271� 0:242

0:4� 0:2

� �0:273� 0:2ð Þ ¼ 0:260

From Eq. (5.1), the total active earth pressure from the fibre-reinforced sand

backfill,

Pa ¼ 1

2KaγH

2 ¼ 1

2

� �0:260ð Þ 15:61ð Þ 8ð Þ2 ¼ 129:9 kN=m

Example 5.2

For a fibre-reinforced foundation sand bed supported by a 1-m wide surface strip

footing, consider the following:

Angle of internal friction of sand, ϕ¼ 30�



Fibre-soil interface friction angle, ϕi¼ 20�


Volumetric fibre content, pvf¼ 1%

Determine load-bearing capacity of the surface strip footing resting over the

fibre-reinforced sand bed, assuming the fibre-reinforced sand behaves as an isotro-

pic material.


Solution

As the fibre-reinforced sand behaves as an isotropic material, the distribution

ratio,

pr ¼ 1

Using the given values,

arpvf tanϕi ¼ 75ð Þ 0:01ð Þ tan 20�ð Þ ¼ 0:273

From Table 5.2, the bearing capacity factor,

Nγ ¼ 33:239þ 53:301� 33:239

0:4� 0:2

� �0:273� 0:2ð Þ ¼ 40:56

From Eq. (5.2), load-bearing capacity of the surface strip footing resting over the

fibre-reinforced sand bed,

qa ¼1

2γBNγ ¼ 1

2

� �15:61ð Þ 1ð Þ 40:56ð Þ ¼ 316:6 kPa

The overall stability of a shallow foundation constructed over the weak founda-

tion soil can be significantly improved by placing a compacted cement-stabilized

fibre-reinforced soil layer of a suitable thickness (say 0.3B, where B being the width

of the footing) over the weak foundation soil as shown in Fig. 5.3. The thickness

may be decided based on the plate load test. The ultimate load-bearing capacity of

this layered soil system can be estimated using the analytical methods proposed by

Vesic (1975) and Mayerhof and Hanna (1978). The later considers a punching

failure along the footing perimeter. Consoli et al. (2003) have reported that Vesic’smethod significantly overestimates the bearing capacity of the footing resting on the

layered system, while Meyerhof and Hanna’s method underestimates it. A research

is required to develop an appropriate bearing capacity equation for determining the

bearing capacity of footings resting on cement-stabilized fibre-reinforced soil layer

over the weak foundation soil.

Note that for the field situation shown in Fig. 5.3, if required, a geosynthetic

reinforcement layer (woven geotextile or geogrid layer) can be installed at the

interface of the cement-stabilized fibre-reinforced soil layer and the weak founda-

tion soil for having additional reinforcement benefits. At several construction sites,

the fibre-reinforced foundation soil with or without geosynthetic reinforcement may

be technically feasible for supporting the structural loads, and additionally they

may have the following advantages:


1. The use of fibres from the waste materials, such as old/used tyres and used

plastic materials, in large quantities, whose presence causes environmental

problems and their safe disposal in engineered landfills costs significantly

2. Reduced foundation cost compared to the cost of deep foundations, such as piles

that carry the loads and transfer them to the rock bed or firm stratum underlying

the weak foundation soil

Young’s modulus is often the dominant parameter for the design of shallow

foundations. Although the fibre-reinforced soil is more compressible than

unreinforced soil, it still complies with the stiffness requirements for several

applications (50–120 MPa), namely, shallow foundations, subgrade, capping or

subbase layers. This compliance means that the fibre-reinforced soil is a suitable

material for construction of these structures. In fact, a reinforced soil exhibits a

suitable bearing capacity and trafficking under the heavy construction machines.

Driving passes of the motor scraper in the close proximity to the borders of fibre-

reinforced embankment confirm the good quality of the reinforced soil as a con-

struction material (Falorca et al. 2011).

Design of fibre-reinforced granular pavement layers requires evaluation of fibre-

reinforced granular materials by the trafficability test, simulating the conditions of

repetitive traffic loading and adverse environment. Details of the test and findings in

terms of variation of average rut depths with number of load cycles are presented by

Hoover et al. (1982) for some fibre-reinforced soils. The findings show that the

inclusion of fibres improves the vertical load stability and prevents lateral shear

and/or displacement for a greater number of load cycles when compared to the

behaviour of unreinforced soil. Further improvement of stability, compressive

characteristics, ductility and control of cracking through brittle failure can be

obtained through addition of cement or lime, mainly due to improved soil-fibre

interfacial bonding. The crimped PP fibres are found to be most effective in

B

Cement stabilized fibre-reinforced cohesionless soil

Strip footing

Load

Weak foundation soil (Saturated soft clay)

Rock

Fig. 5.3 A strip footing resting on a cement-stabilized fibre-reinforced cohesionless soil layer

over a weak foundation soil stratum


improving the engineering characteristics of soil. The scanning electron micros-

copy shows that the straight PP fibres exhibit severe surficial damage after com-

paction and testing, and the glass fibres appear undamaged.

Benefits of reinforcing the pavement layers (subgrade, subbase course and/or

base course) with fibres (or other reinforcement types) are generally expressed in

terms of an extension of service life of the pavement and/or a reduction in the

thickness of pavement layer. An extension of service life of the pavement is

typically expressed in terms of the traffic benefit ratio (TBR), which is defined as

follows (Perkins and Edens 2002):

TBR ¼ NR

NU

ð5:3Þ

where N is the number of traffic loads/passes required for producing a pavement

surface deformation (i.e. rutting) up to the allowable rut depth for the pavement and

the symbols U and R denote unreinforced and reinforced pavement sections,

respectively. Thus, the TBR basically indicates the additional traffic loads/passes

that can be applied to the pavement with fibre-reinforced layer, with all other

pavement materials and geometry being equal.

The benefit of reinforcing in reduction in the thickness of pavement layer

(subbase course, base course and/or surface course) is typically expressed in

terms of layer reduction ratio (LRR), which is defined as follows:

LRR ¼ DU � DR

DU

ð5:4Þ

where DU and DR are the pavement layer thickness of the unreinforced and fibre-

reinforced pavement sections, respectively, for equivalent service life. If the layer is

base course, the layer reduction ratio (LRR) may be better called base coursereduction ratio (BRR) as considered by Perkins et al. (2002).

The pavement can also be designed for any intermediate thickness to reduce the

thicknesses of the pavement layers and/or to gain additional benefits in terms of

extension of the service life of the pavement. For example, by reinforcing the

subgrade soils, the thickness of the subbase course can be reduced as required. If

a reduction in the thickness of the subbase course is not required, then with fibre

inclusions into subgrade soils, the benefits can be achieved in terms of TBR. Thusthe actual advantage of fibre inclusions depends upon the option exercised by the

pavement designer (Chandra et al. 2008).

For the design of a pavement structure, repeated dynamic load test may be

conducted in a model test tank as Kumar and Singh (2008) presented their work

using a steel tank of size 0.6 m � 0.6 m � 0.6 m and creating a pavement structure

with subgrade, subbase and base courses. Wet Mix Macadam (WMM) was used as

the base course. For the rural roads, the traffic load was considered the medium load

(41 kN). The number of load cycles applied on the top of the base course was

limited to 10,000 only. Table 5.3 shows the deformation of the top surface of the


base course for different combinations of subbases of fly ash (silt of low compress-

ibility, ML) and local soil (poorly graded fine sand, SP) with PP fibres. Note that the

rut depth is an indicator of the life of the pavement. A reduction in the rut depth due

to loading shows more expected life. Fly ash alone has 6.07-mm rut depth, but in the

case of fly ash with 25% soil and 0.2% fibres, rut depth is nearly half of the rut depth

in the case of fly ash only.

Jha et al. (2014) analysed the benefit of reinforcing the industrial waste materials

(fly ash, stone dust and waste recycled product) with HDPE plastic waste strips in

terms of LRR for their applications as the subbase course material in the construc-

tion of flexible pavements. Their analysis shows that with inclusion of plastic waste

strips into industrial wastes, the thickness of subbase course can be reduced up to

50%, depending on the service life and site requirements. The reduced thickness of

the pavement layers results in lower total cost of the pavement and lower construc-

tion time, thus consuming reduced quantities of natural soil and materials for

construction and hence providing an environmentally friendly solutions in a sus-

tainable manner.

Permeability is the most important design parameter for water-retaining struc-

tures. The effect of fibre inclusions in soil on its permeability has been presented in

Sect. 3.6. In general, inclusion of fibres in soil decreases its coefficient of perme-

ability (a.k.a. hydraulic conductivity), and hence this benefit can be used in reduc-

ing the seepage through the body of water-retaining soil structures. Babu and

Vasudevan (2008) have explained the benefits of mixing coir fibres into red soil

used for the construction of a temporary check dam over an impermeable bed

(Fig. 5.4). The seepage analysis shows that an increase in fibre content decreases the

discharge per unit length of the dam (Fig. 5.5). Thus the coir fibres are effective in

controlling the seepage through the body of check dams, which are often

constructed for the water conservation purposes in many countries.

Sheet pile walls have several applications in civil engineering as permanent and

temporary structures. A sheet pile wall embedded in a soil is often used to retain

water. Babu and Vasudevan (2008) have also explained the benefits of replacement

of the soil deposit by coir fibre-reinforced soil on the downstream side of the sheet

pile wall (Fig. 5.6). The analysis for soil piping shows that as the fibre content in

soil increases, the factor of safety against the piping failure, as determined from

Eq. (1.27), also increases (Fig. 5.7). The maximum exit hydraulic gradient may be

calculated using the following relationship (Harr 1962):

Table 5.3 Rut depth in a model section after 10,000 cycles in each case

Combination of subbases Rut depth (mm) Percentage decrease in rut depth

Fly ash only 6.07

Fly ash + 0.2% fibres 4.29 29

Fly ash + 0.3% fibres 3.25 46

Fly ash + 25% soil 4.44 27

Fly ash + 25% soil + 0.2% fibres 3.20 47



ie ¼ H

3:14Dð5:5Þ

where H is the total head lost in the flow and D is the depth of penetration of sheet

pile wall. Equation (5.5) is based on the assumption that the impermeable layer is

available at a shallow depth.

Impermeable stratum


Fig. 5.4 A check dam constructed with coir fibre-reinforced red soil

0 0.2 0.4 0.6 0.8 1.0 1.20

0.4

0.8

1.2

1.6


Coir fibre length = 50 mm

Dis

char

ge p

er m

etre

leng

th (m

3 day-1

m-1

)

Fig. 5.5 A typical variation of discharge per unit length of the check dam, constructed with coir

fibre-reinforced red soil over an impermeable stratum, with fibre content (Adapted from Babu and

Vasudevan 2008)

Note: Base width of dam ¼ 10 m; height of dam ¼ 2 m; top width of dam ¼ 2.48 m; side sloping

angle ¼ 28�; dry unit weight of soil ¼ 14.3 kN/m3; moulding water content ¼ 17.8%; and free

board ¼ 0. 2 m


Desiccation cracking of soil is a problem encountered in many engineering

disciplines, including geotechnical and geoenvironmental engineering. Desiccation

of landfill clay liners is a major factor affecting landfill performance. Desiccation

leads to the development of shrinkage cracks. The cracks provide pathways for

moisture migration into the landfill cell and thus increases the generation of waste

leachate and ultimately increases the potential for soil and groundwater contami-

nation. For liner design applications, Miller and Rifai (2004) presented the concepts

Sheet pile wall


Impermeable stratum

Fig. 5.6 A sheet pile wall with compacted coir fibre-reinforced soil on the downstream side

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.60

1

2

3

4

5

6

7

8

Sand

Red soil

50% Red soil + 50% sand


Fact

or o

f saf

ety

agai

nst p

ipin

g, F

S pip

ing Coir fibre length = 50 mm

Fig. 5.7 Effect of fibre content on factor of safety against piping failure for the sheet pile with coir

fibre-reinforced soil on the downstream side (Adapted from Babu and Vasudevan 2008)

Note: Embedded depth ¼ 2 m; upstream water depth ¼ 2.5 m; downstream water depth ¼ 0.5 m


of crack evaluation. The following terms can be used to assess the liner crack

potential:

1. Crack intensity ratio (CIR): It is defined as the ratio of cracked area (AC) to the

total surface area (A) of the soil, that is,

CIR ¼ AC

Að5:6Þ

The value of CIR is normally expressed as a decimal.

2. Crack Reduction Factor (ICR): It is defined as

ICR ¼ CIRU � CIRR

CIRU

ð5:7Þ

where CIRU is the crack intensity ratio for unreinforced soil and CIRR is the crack

intensity ratio for fibre-reinforced soil. The value of (ICR) is normally expressed as a

percentage.

For landfill applications, Miller and Rifai (2004) studied the effect of PP fibre

reinforcement (length varying from 0.5 to 2 in.) on desiccation cracking of medium

plasticity soil (classified as CL with liquid limit ¼ 40 and plasticity index ¼ 17)

compacted at 2% wet of the optimum water content as a function of fibre content

and crack reduction. The relationship between crack reduction and fibre content

(Fig. 5.8) shows that increasing the fibre content, from 0.2 to 0.8%, significantly

increases the crack reduction, from 12.3 to 88.6%, respectively. The slope of the

curve in Fig. 5.8 suggests that increasing the fibre content would have increased the

crack reduction further. However, exceeding a fibre content of 0.8% is not practical

due to difficulty in fibre-soil mixing to obtain uniform distribution of fibres within

the soil. The cracks are observed wider and more intensive in the natural soil

specimen than those shown in the fibre-reinforced soil specimen. The cracks in

the latter are so small that they are barely visible.

The magnitude of hydraulic conductivity of clayey soil should be one of the

primary characteristics used to judge its acceptability for containment structures

(i.e. landfill covers and bottom liners). Therefore, it is critical that the effect of fibre

inclusion on the hydraulic conductivity of the clayey soil should be evaluated as one

of the design steps for covers and liners. Miller and Rifai (2004) conducted

hydraulic conductivity test on a medium plasticity soil (classified as CL with liquid

limit ¼ 40 and plasticity index¼ 17) using modified compaction effort and 2% wet

of optimum water content. The tests were performed using fibre contents of 0.0, 0.2,

1.0, 1.5 and 2.0%. The test results, as presented in Fig. 5.9, indicate that the

hydraulic conductivity of the fibre-reinforced soil is dependent on the fibre content,

generally increasing with fibre content increase. The slight decrease of hydraulic

conductivity noted around 0.2% fibre content is within the limits of experimental

error and should not be used to infer that minor fibre additions improve the


hydraulic conductivity. The increase in hydraulic conductivity is most significant

for fibre contents exceeding 1%.

Note that the optimum fibre content that is necessary to achieve the maximum

crack reduction, maximum dry unit weight and acceptable hydraulic conductivity

within the range of mixing workability is found to be between 0.4 and 0.5% in the

experimental study conducted by Miller and Rifai (2004).

5.4 Field Application Experience and Guidelines

Influences of the engineering properties of soil and reinforcement and the scale

effects on the properties of the fibre-reinforced soils have not been investigated

fully, and hence the actual behaviour of fibre-reinforced soil is not yet well known.

The large-scale investigations for all possible applications of fibre-reinforced soil

are limited in the literature, and hence they are the subject of further study. Thus,

the use of randomly oriented discrete fibres for different applications, as described

here, requires investigations at a large scale.

Park and Tan (2005) conducted full-scale tests on a retaining wall with PP fibre-

reinforced soil backfill (with 0.2% fibre content), with and without geogrid

reinforcement (tensile strength of 50 kN/m in machine direction and 20 kN/m in

cross machine direction), in Korea Railway Research Institute, using a large soil

box (22 m in length, 5 m in width and 3 m in depth), a loading frame and a reaction

plate. The test was fully instrumented with earth pressure cells, displacement

gauges, load cells and settlement plates. The numerical model of the wall with

0 0.2 0.4 0.6 0.8 1.00

20

40

60

80

100


Cra

ck re

duct

ion

fact

or, I

CR

(%)

Fig. 5.8 Variation of crack reduction factor for a medium plasticity soil with fibre content

(Adapted from Miller and Rifai 2004)

5.4 Field Application Experience and Guidelines 161

reinforced backfill was also developed using a finite element programme

(2D PLAXIS version 7.2). Some of the key observations are given below:

1. Distribution of vertical earth pressure is almost the same for all cases of

unreinforced as well as reinforced soil system. When a load is applied on the

backfill, the fibre-reinforced soil backfill shows slightly smaller vertical stress

increase compared to unreinforced soil.

2. Immediately after construction, and upon loading, the fibre-reinforced soil

backfill without geogrid appears to have the smallest horizontal pressure

distribution.

3. Wall deflection is smaller if the fibres are included within the backfills. The

presence of geogrid reinforcement reduces the wall deflection further to some

extent, but very small reduction in deflection cannot justify the cost of using

geogrid reinforcement along with fibres.

The fibre-reinforced compacted soil backfill is thus stronger and stiffer than

unreinforced compacted soil backfill. Inclusion of geosynthetic reinforcement layers

within the fibre-reinforced soil backfill can lead to an economical construction of

very high retaining wall, even with a vertical face, especially in built-up areas.

At some sites, shallow foundations and pavements are often constructed along

the ground supported by sheet pile walls or other retaining structures, as shown in

Fig. 5.10. Nasr (2014) studied experimentally and numerically the potential benefits

of reinforcing the poorly graded sand backfills at a relative density of 50% in the

active zone behind a model steel sheet pile wall (750 mm long, 499 mm wide and

3.3 mm thick) by using PP fibres (12 mm long, 0.023 mm thick) and cement kiln

dust (15.42% SiO2, 3.92% Al2O3, 2.95% Fe2O3, 51.23% CaO, etc.). The test

involved loading a rigid strip footing (499 mm long, 100 mm wide and 25 mm

thick) resting on the sand backfill surface in the active zone adjacent to the sheet

pile wall in a steel test tank (1.5 m long, 0.5 m wide and 0.9 m high). The sheet pile

0 0.5 1.0 1.5 2.01.0E-10

1.0E-09

1.0E-08

1.0E-07

1.0E-06

1.0E-05


Hyd

raul

ic c

ondu

ctiv

ity, k

(m/s)

Fig. 5.9 Variation of hydraulic conductivity of medium plasticity soil with PP fibre content

(Adapted from Miller and Rifai 2004)


wall was embedded 500 mm in the sand bed. The results obtained from the study

suggest the following:

1. Addition of PP fibres to the cemented sand increases the ductility as indicated by

the increase in deformability index Di. For lower fibre content (� 0.5%), Di is

weakly influenced by the cement kiln dust content.

2. The presence of fibres in the cemented sand backfill behind the sheet pile wall

decreases the lateral deflection of the wall significantly. For the cement kiln dust

content (as per Eq. (2.9)) of 9%, the maximum lateral deflection decreases by

about 51% at a fibre content (as per Eq. (2.10)) of 0.75%.

3. Ultimate bearing capacity of the strip footing resting on the fibre-reinforced

cemented sand in the active zone increases with an increase in the thickness of

reinforced sand layer. However, for higher fibre content (� 0.75%), an increase

in ultimate bearing capacity is not significant at a thickness h of fibre-reinforcedcemented sand layer greater than 0.4H(H¼ wall height; see Fig. 5.10).

4. Increasing the distance between the strip footing and the sheet pile wall leads to a

significant increase in ultimate bearing capacity of the footing and a decrease in

the maximum lateral deflection of the sheet pile wall. However, for higher fibre

content (� 0.75%), if the distance s between the strip footing and the sheet pile

wall is more than 0.8H, there is no appreciable increase (about 4.8%) in ultimate

bearing capacity of the footing.

Sand and sandy gravels are generally not used in the top courses (high level of

base course or surface course) of pavements although they are easily available at

several construction sites because their properties do not meet the technical require-

ments of top courses. In order to utilize sand as a construction material on a larger

scale in the top courses, sand can be reinforced with short fibres by mixing sand and

fibres by the mix-in-plant process. Lindh and Eriksson (1990) provided the details

of a pilot experiment performed in 1988 on two pavement test stretches, 20 m and

40 m, by incorporating a 100-mm layer of sand in the pavement mixed with short

(48-mm) plastic fibres at 0.25 and 0.5% fibre contents, respectively. Sand, water

and plastic fibres were mixed successfully in a concrete mixing plant of the drum

Fibre-reinforced soil backfill layer

Strip footing

Fibres

Load

Passive zone

Active zone

Sheet pile wall

Hh

s

Fig. 5.10 Loaded active zone adjacent to a sheet pile wall (Adapted from Nasr 2014)


mixer type. The 100-mm reinforced sand layer was applied directly on the old road

surface. A 100-mm layer of base course gravel was applied on the sand layer,

followed by a surface dressing (see Fig. 5.11). Prior to applying the fibre-reinforced

sand, the grading curve of the material in the surface layer of the old road was

improved by mixing in macadam. The spreading and rough levelling of the fibre-

reinforced sand were performed with a grader. The normal shaping could not be

performed on the reinforced sand as it became matted, and adhered to the shaper in

lumps. The final shaping of the surface therefore had to be performed with hand

tools. After compaction, the fibre-reinforced sand had considerably better stability

than the layers of packed sand, and showed no rutting of the road surface during

about the first 2 years’ use by traffic; thus the test stretches performed well. With

inclusion of fibres, the sand absorbs tensile strains and can therefore improve

resistance to permanent deformation of sand layer when loaded.

Santoni and Webster (2001) described the laboratory and field tests conducted

using a new fibre stabilization technique for sands. Laboratory unconfined com-

pression tests using 51-mm long monofilament PP fibres to stabilize a poorly graded

(SP) sand showed an optimum fibre content of 1% (by dry weight). The field test

sections were constructed and traffic tested using simulated C-130 aircraft traffic

with a 13,608 kg tyre load at 690 kPa tyre pressure and a 4536 kg military cargo

truck loaded to a gross weight of 18,870 kg. The test results showed that the sand-

fibre stabilization over a sand subgrade supported over 1000 passes of a C-130 tyre

load with less than 51 mm of rutting. The top 102 mm of the sand-fibre layer was

lightly stabilized with tree resin to provide a wearing surface. Based on limited

truck traffic tests, 203-mm thick sand-fibre layer, surfaced with a spray application

of tree resin, would support substantial amounts of military truck traffic.

Tingle et al. (2002) reported the details of two field test sections to evaluate the

ability of fibre-stabilized sand beds to sustain military trucks. It is observed that the

fibrillated fibres provide the best rut resistance, followed by the monofilament, the

tape and then the Netlon mesh elements. The 0.8% fibre content recommended by

Santoni et al. (2001) showed to provide adequate structural support for the test

traffic. Slightly better performance was noted at a fibre content of 1%, but the slight

increase in rut resistance did not justify the added cost of the additional fibres. The

Single surface dressing100 mm base course gravel

100 mm sand reinforced with 48 mm plastic fibres

Macadam mixed in the existing road material

New layers

Fig. 5.11 Longitudinal test section of road pavement (lengths of 20 m and 40 m with the use of

plastic fibre contents of 0.25% and 0.5%, respectively, in the sand layer) (Adapted from Lindh and

Eriksson 1990)


field tests demonstrated similar performance between 51-mm (2 in.) and 76-mm

(3 in.) fibre lengths, but the 76 mm tended to hand up on the mixing equipment.

Thus, 51-mm fibre length appears to be more appropriate for field use. In general,

the design criteria for unsurfaced roads are based on the development of a 76-mm

(3 in.) rut upon completion of the design traffic. The amount of rutting, 63–89 mm

(2.3–3.5 in.), exhibited in the field tests indicates that the design thickness of

203 mm (8 in.) was appropriate for the design traffic, except for the case with the

Netlon mesh fibres. The test sections demonstrated the need for a surfacing for

fibre-stabilized layers to keep the tyre friction from pulling the fibres out of the

sand. Road Oyl provided a good wearing course for the applied traffic. Cousins Pine

Sap Emulsion and PennzSuppress D also provided adequate resistance to fibre

pullout. The hexagonal mat surfacing provided an adequate wearing course, but

no additional structural strength was provided by the mat since the sand had already

been confined by the fibres. Note that the majority of the permanent deformation or

rutting that occurred during the test period consisted of densification of the stabi-

lized sand and supporting sand layers.

Based on the available experience and studies reported in the literature as well as

the author’s experience, some application guidelines are given below:

Care and Consideration

• There are a large number of factors and variables that affect the engineering

behaviour of fibre-reinforced soils. The stress-strain properties of fibre-

reinforced soils are functions of fibre content, aspect ratio and skin friction

along with the soil and fibre index and strength characteristics and confining

pressure. Thus, the design and construction of fibre-reinforced soil structures

should properly consider all these variables.

• Because of the major influence of confining stress, the design parameters should

be based on the triaxial compression tests, especially on the large-size

specimens.

• The method of fibre-reinforced soil placement should be similar to the method

used for preparing the fibre-reinforced soil specimens for the tests conducted to

obtain the design parameters. This is essential to maintain the fibre orientations

the same in both the tests and field applications.

• In general, fibres are most influential when orientated in the same direction as the

tensile strains. Therefore, for any particular loading condition, the effectiveness

of fibre inclusions depends on their orientation, which in turn depends on the

sample mixing and formation procedure. However, an attempt should be made to

make the reasonably uniform distribution of the fibres within the soil mass.

• The in situ mixing and compacting may cause preferred near-horizontal orien-

tations; hence, the properties of fibre-reinforced soil are anisotropic to some

extent.

• The consequence of an assumed isotropy as generally expected in the soil-fibre

mixes may result in an overestimation or underestimation of reinforced soil

design parameters, depending on the direction of practical importance.

• Since the limited settlement is generally the design criterion for actual founda-

tions on soil, a comparison of the bearing pressure values at some selected


settlement levels for the reinforced and unreinforced cases should be made for

the design purpose.

• Site-specific laboratory and field tests should be conducted to determine the

design parameters/variables.

• As several contradictory observations/conclusions have been reported in differ-

ent studies, they should be used carefully in analysis and design of fibre-

reinforced structures.

• As the significant influence of fibre reinforcement on the ultimate strength of

fibre-reinforced soil continues to be observed even at very large shear strains

(horizontal displacements) in the laboratory study, there is no tendency to lose

strength, and the fibre-reinforced soils would therefore be unlikely to suffer from

brittle failure in field applications even in cases where the strains localize, as

they do in a ring shear apparatus. Thus there is a great potential of PP and other

similar fibres as the soil reinforcement (Heineck et al. 2005).

• The use of natural fibres such as coir and jute fibres may make possible construc-

tions, such as embankments and bunds, rural road bases, etc., cost-effective and

environmentally friendly, especially in applications for short duration of 2–3 years

in order to have short-term stability. Of most natural fibres, coir has the greatest

tearing strength and retains this property even in wet conditions.

Mixing, Placement and Compaction

• The simplest method of mixing fibre and soil in a rotating drum mixer does not

result in a uniform mixture due to a large difference in specific gravities of

fibre and soil. The drum mixing method usually results in the segregation or

floating of fibres even when some water is added. In fact, because of the

lightweight and low specific gravity of fibres (for some types it can be even

less than unity) compared to soil particles, the fibres cannot be uniformly

distributed in the mixture during drum rotation.

• The effective method of fibre inclusion can be spraying the fibres over each soil

lift during field compaction, especially in pavement bases and subbases. The

main advantages of fibre reinforcement in bases and subbases are increase in

load-carrying capacity, reduction in rut depth, reduced cost, etc.

• One of the most satisfactory mixing techniques can be provided by blowing

fibres into a rotary mixer chamber with a mulch spreader equipped with a

flexible hose. Blade mixing provides a reasonable satisfactory random distribu-

tion of fibres (Hoover et al. 1982).

• Mixing is a critical factor in the case of discrete, randomly oriented fibre

reinforcement. Blade- or paddle-type mixers do not work as they tend to drag

and ball up the fibres. Vibratory mixers tend to float the fibres up. A special

oscillatory or helical action mixer can be used to avoid these problems; but even

this type of mixer has limitations on the maximum fibre content that can be

uniformly and randomly distributed in the mix. The degree of randomness in the

mixture may be determined by visual inspection (Gray and Al-Refeai 1986).

• Compared to hand mixing, the z-blade mixer produces suitable even mixes of

clay and PP fibres within a reasonable time (Gelder and Fowmes 2016).


• Water content of the soil should be lower than the optimum water content

corresponding to the level of compaction required to facilitate pulverization of

the soil particles.

• In order to easily mix the fibres uniformly, the initial/natural water content of the

cohesive soil may be increased to optimum mixing moisture content (OMMC)

prior to the introduction of fibres if lime has to be added. By introducing

quicklime, excess moisture is removed through the hydration (exothermic reac-

tion) process, thus improving the workability of soil. If lime is not added, the

mixture should be allowed for air drying at the site to get the moisture content

reduced to the target value (Gelder and Fowmes 2016).

• For preparing a good-quality mixture of fibres and clayey soil, the water content

of the soil may be kept near its plastic limit, which may fall on the wet side of the

compaction curve (Falorca and Pinto 2011).

• For proper mixing of fibres with soil, water required to obtain the target water

content should be added to soil prior to placing the fibres on the soil. This is done

to keep the fibres from sticking together during mixing (Tingle et al. 2002).

• Higher fibre content, longer fibres and crimped fibres can make the mixing

procedure more difficult.

• Compaction of soil fibres can be done in two stages: one pass of the motor

scrapper followed by 4–6 passes of a roller.

• A vibratory rubber-tyred roller may be most suitable for the compaction of fibre-

reinforced soils (Falorca et al. 2011).

• More compaction energy may be necessary to produce specimens with higher

fibre contents at a given dry unit weight. Thus, the fibre-reinforced soil may

provide an increased resistance to compaction, even in field compaction.

• In general, for the embankment construction, the soil-fibre mixture should be

produced and placed in a single step only. It is not feasible to spread and level the

mixture by maintaining the homogeneity, as some clods of fibres are produced

and dragged by the motor scraper. The reinforced layers must therefore be ready

for compaction immediately after placement, with no need for levelling pro-

cedures. For a better uniform distribution of fibres within the compacted soil

mass, the soil and fibres may be spread in a sandwich pattern and then mixed

with a rotary tiller, in the following steps (Falorca et al. 2011):

• The predetermined quantity of fibres is spread uniformly by hand or other

suitable means over the surface.

• The necessary amount of soil is then spread over the fibres.

• Finally, the rotary tiller is driven along the entire area of the section in a

regular pattern at a slow speed, combined with high rotation, in order to have

a satisfactorily homogeneous mixture.

These steps can be repeated until a 0.2-m thick layer is completed. The number

of sub-layers needed to complete a 0.2-m thick layer is found to depend on the fibre

characteristics. This procedure becomes impractical when the number of sub-layers

is greater than six. For the highest fibre content and lowest fibre diameter, the


maximum number of fibres needs to be mixed with the soil. This is the most difficult

situation, which requires the highest number of sub-layers.

• A thin top soil layer of about 50-mm thickness should be placed over the entire

surface area of the embankment to protect the synthetic fibres, such as PP fibres

from UV degradation. The top soil layer also helps minimize fissures which may

be caused by a recovering deformation of the reinforced soil (Falorca et al.

2011).

• In pavement base/subbase construction, the selected type and amount of fibres

should be weighed and can be uniformly spread by hand across the surface of the

moist base/subbase material. Four to six passes of a self-propelled rotary mixer

should be initially used to mix the fibres with base/subbase material. Then the

material should be piled and releveled, and four to six additional passes of the

rotary mixer should be used to uniformly mix the fibres with the material. The

fibre-reinforced material should then be dumped in place as required for com-

paction by rollers.

• If required, the individual fibres from the yarns can be separated by first,

punching a few holes with a paper hole punch near the closed end of a large

(say, 125 L) plastic bag. Next, a handful of yarn fibres are placed in the bag. The

bag is hand-held closed around an air nozzle and inverted, and air is blown

through the fibres. The air separates the fibres from the yarn effectively and

promptly. The separated fibres form the fluffy bundles that resemble cotton

candy (Santoni and Webster 2001).

• When tyre chips are used, construction activities may be eased by specifying tyre

chips less than 75 mm (maximum dimension). For compaction of tyre fibre-

reinforced soil, vibratory roller should not be specified. Compaction specifica-

tions should not be based on a final unit weight, but the optimum number of

passes should be determined based on a test section in the field. Compressibility

is the governing parameter in designing structural fills using tyre chips. To

achieve minimum compressibility, a minimum soil cover thickness of 1 m

over the tyre chips should be specified. The use of a geotextile to separate the

cover soil from the porous tyre chip fill is recommended to prevent migration of

the soil into the tyre chips pores. Sand-tyre chips mixtures exhibit higher moduli

than clay-tyre chips mixtures at the same soil-tyre chips ratio (Edil and Bosscher

1994).

Durability

• Attempts are being made to increase the long-term durability of fibres in a cost-

effective way, such as coating of fibres with phenol and bitumen, and probably in

the future, several coating methods will be available. However, natural fibres can

be used routinely in less critical applications (e.g. pavement bases/subbases) or

short-term applications (e.g. erosion control).

• The surface of fibres may be made rough by cementing a layer of suitable

materials, such as fine sand particles, to the fibres for achieving a full mobiliza-

tion of soil angle of internal friction during shearing.


• Natural fibres may be protected from biodegradation by coating with suitable

materials. Ahmad et al. (2010) coated oil palm empty fruit bunch (OPEFB)

fibres with acrylonitrile butadiene styrene (ABS) thermoplastic for increasing

the resistance to biodegradation. A layer of coating on a fibre also increases its

diameter and the surface area, resulting in increased interface friction of fibre

and soil as well as the fibre tensile strength. Hence, as an additional advantage,

the inclusion of coated OPEFB fibres in silty sand increases its shear strength

much more compared to uncoated fibres, as reported by Ahmad et al. based on

the results obtained from consolidated drained and undrained triaxial compres-

sion tests. Sarbaz et al. (2014) used bitumen-coated palm fibres for reinforcing

fine sand and studied the effect of bitumen coating on the CBR strength of sand.

Application Experience

• Stability of retaining walls under dynamic load conditions may require the use of

more stable backfills. For increase in stability of walls by the reduction of lateral

earth pressure, short fibres (say, 60-mm long PP fibres) may be included ran-

domly in soil backfills (Park and Tan 2005). The beneficial effect can be more to

some extent when short fibres are used in combination with geogrid reinforce-

ment within the backfill.

• Inclusion of tyre chips (20 mm long, 10 mm wide and 10 mm thick; specific

gravity¼ 1.08 and unit weight¼ 6.45 kN/m3) up to 30% by weight in the poorly

graded sand backfill behind the wall effectively works to reduce the wall

displacements and lateral earth pressures against the wall by about 50–60%,

thereby resulting in reduced dimensions of the wall (Reddy and Krishna 2015).

• Shallow foundations on fibre-reinforced cohesionless/granular soil deposits

should be designed based on the findings of large-scale model footing tests or,

if possible, by testing full-scale trial footings; otherwise, a simple test may be

devised, for example, in the form of measuring the imprint dimensions or the

penetration depth of a falling object (Wasti and Butun 1996).

• Even though the sand-cement layer provides a higher bearing capacity when

compared to cement-stabilized fibre-reinforced sand layer, the latter, in terms of

post-peak behaviour, leads to a more reliable solution and possibly to a reduction

in the design safety factor, because the fibre inclusion reduces dramatically the

brittle response of the foundation soil system (Consoli et al. 2003).

• The beneficial effects of fibre reinforcement in soil can be enhanced significantly

by stabilizing the fibre-reinforced soil with cement in a suitable quantity, say

using cement content of 5–10%.

• The footing or pavement load should be placed suitably away from the retaining

structure to get maximum benefits from inclusion of fibres in terms of increase in

the load-bearing capacity of the footing.

• The granular pile and trench, which are used for stabilizing the weak clayey

foundation soil, can be strengthened by inclusion of fibres in place of reinforcing

them by layers of geosynthetic reinforcement (Gray and Al-Refeai 1986).

• With increase in shear strength of soil with inclusion of fibres, a steeper slope

may be constructed, resulting in saving of the land area, which may be utilized


suitably. The slope stability analysis of the fibre-reinforced slopes may be

carried out using the discrete approach, which considers the fibre-induced

distribution of tension parallel to the failure plane along with the soil shear

resistance separately.

• Decrease in rut depth, which is an indicator of increase in the life of pavement,

takes place as a result of inclusion of fibres in soil and other similar materials

such as fly ash.

• Stabilization of sand with discrete fibres is a viable alternative to traditional

stabilization techniques for low-volume road applications. Fibre stabilization

requires less material (fibre additives) by dry weight than most traditional

stabilization techniques. The construction and maintenance techniques have

been shown to be practical and successful in terms of maintaining the service-

ability of the road. However, the densification of fibre-stabilized materials under

repeated traffic loadings may limit the applicability of this technology for use in

situations in which settlements and deformations cannot be tolerated (Tingle

et al. 2002).

• During trafficking by the heavy construction machinery, in terms of depth of

ruts, the fibre-reinforced soil sections are observed to be more stable than the

unreinforced sections.

• In case of rural roads, the subbase material should have a minimum soaked

CBR of 15%. Fly ash reinforced with PP fibres with 0.2% fibre content has been

found to have CBR of 16.6%; therefore, this is suitable for rural road subbases.

Fibre content can be reduced to 0.1% if fly ash is mixed with 25% of poorly

graded fine sand (SP) (Kumar and Singh 2008).

• Cement-stabilized soils are often used as pavement base courses, backfills

behind retaining walls, embankments and foundation. As the cement content

increases, the strength properties of soil improve significantly, but an increase in

cement content causes a brittle or sudden failure without a plastic deformation.

As the brittle/sudden failure is undesirable in engineering applications, for

preventing the brittle failure, fibres may be added to cement-stabilized soil in a

suitable quantity with a random distribution.

• Fibre inclusionswith an optimum aspect ratio increase theCBR of the soil subgrade/

subbase/base courses and hence may cause a substantial decrease in design thick-

ness of the pavement layers, thus making the pavement project economical.

• Fibre inclusions mixed with soil subgrade also provide needed tensile strength

under traffic loads.

• The fibre reinforcement of roadway soils should be associated with base or

subbase courses having adequate surfacing (Hoover et al. 1982).

• Shredded waste tyres can be used as soil subgrade reinforcement, aggregate in

leach beds for septic systems, additive to asphalt, substitute for leachate collec-

tion stone in landfills, daily cover materials in landfills, lightweight fills, edge

drains, etc.

• The CBR values decrease significantly as the amount of tyre buffings (gradation

between 1.0 mm and 12.5 mm) increases in the subbase gravel (crushed stone,

classified as well-graded gravel, GW). Subbase gravel with 3% cement and 5%


tyre buffings give higher CBR values than gravel alone. The use of gravel, tyre

buffings and cement can reduce the tyre disposal problems in pavement granular

courses (Cabalar and Karabash 2015).

• In pavement applications, the stabilization of cohesionless materials, such as

sand and gravel, with discrete fibres requires that some form of surfacing should

be used as a wearing course to prevent the fibres from being pulled out of the

sand/gravel during trafficking if used as the surface layer of the pavement

structure, especially in unsurfaced (unpaved) pavements. Friction forces

imparted on the surface of the pavement by the vehicle tyres tend to pull the

individual fibres from the sand and gravel over time. As the fibres are withdrawn

out of sand and gravel, the reinforcement of the stabilized layer is degraded

(Tingle et al. 2002). Resin-modified emulsion, biodegradable emulsion com-

posed of tree sap and water-emulsified resin base are some examples of spray-on

materials available commercially under different trade names. Different types of

ultraviolet ray-resistant plastic mat panels are also available in the market for use

as surfacings.

• The cement-stabilized fibre-reinforced soil may be used to construct the top

layers of an embankment if it has to support a pavement or any other

structural load.

• The monofilament fibres show a great potential for use in rapid stabilization of

sandy soils for pavement base/subbase applications. The field demonstration

tests should be carried out to test fibre stabilization performance under actual

road/air traffic landing. The field tests should also be conducted to test the

durability and maintenance requirements for sand-fibre pavement layers

(Santoni and Webster 2001).

• The laboratory investigations carried out by Santoni et al. (2001) indicate the

optimum conditions for fibre reinforcement to include the following: a dirty sand

with 1–4% silt; the use of 51-mm (2 in.) long fibrillated fibres at the smallest

available denier; a fibre content of 0.8% by dry weight; fibres and soil mixed at

� 2% of optimum water content of the of the composite material.

• In general, the addition of cement significantly increases the strength of soil

under both static and dynamic loads, contributes to the volume stability, and

increases the resistance to liquefaction in fine sandy and coarse silty soils. The

strength of cement-stabilized soil can further be increased significantly by

addition of fibres.

• For reinforcing the black cotton soils with glass fibres, the maximum fibre

content can be limited to 2% by weight to achieve the optimum benefits (Gosavi

et al. 2004).

• Since a potential use of fibre-reinforced cohesive soil is in landfill liners and

covers, it is important to assess the effect of specific fibre inclusion on hydraulic

conductivity of soil.

• For achieving more tensile strength of fibre-reinforced clayey soil, with a given

fibre content, shorter and better dispersed fibres should be used (Maher and Ho

1994).


• PP and glass fibre reinforcements can be used in kaolinite clay beams undergo-

ing flexural load to limit the cracks and increase the toughness (Maher and Ho

1994).

• Fibres can be mixed into soil for making embankment dams and other water-

retaining structures more resistant to piping erosion, provided the optimum fibre

content is selected based on a suitable piping test. A high fibre content, say

greater than 0.15% for PP and PET fibres, may be harmful and may actually

reduce the piping resistance (Das and Viswanadham 2010).

• A cluster of fibres in one location within the soil, which may take place with high

fibre content, can result in increased permeability, reduced piping resistance and

reduced strength.

• Dredging of sediments and dewatering of the dredged sediment/slurry through

the geotextile tubes is common engineering tasks in several countries. A varia-

tion in slurry particle sizes, particularly fine-grained particles, creates issues with

soil loss and dewatering rates within the geotextile tubes. The dewatering rate

and final filter cake properties have the most importance to dewatering applica-

tions. The faster the flocculated sediments settle and dewater, the quicker the

next geotextile tube can be filled. The pressure filtration tests show that the

dewatering time decreases significantly with inclusion of 0.5% of both nylon and

jute fibres, but is not dependent on the fibre length. However, the increase in

shear strength of filter cake is dependent on fibre length. Jute fibres do not show a

high strength gain as the nylon fibres but increase the dewatering times by an

average of 14–22% compared to filter cakes with nylon fibres. One possible

explanation for variations in dewatering rates between nylon and jute fibres can

be by the fact that jute fibres have a larger diameter and overall surface area,

which allows for more soil-fibre interaction, thereby causing an increase in void

volume through which water can pass easily and, therefore, expedite the

dewatering rate (Spritzer et al. 2015).

• Fibre reinforcement would be an efficient method in limiting or even preventing

the occurrence of the lateral movement of the sandy soils due to liquefaction as

normally observed for unreinforced sands (Noorzad and Amini 2014).

Quality Control

• Regular visual inspections should be carried out to control the randomness and

both the horizontal and vertical uniformity of the fibre distribution. The actual

fibre content at different locations should be checked by suitable methods and

compared with the design fibre content.

• While constructing the fibre-reinforced soil structure, the fibres should be

introduced in each sub-layer by mixing the amount of fibres with soil as per

the designed content.

• The compaction control through the dry unit weight measurement is of little

interest for fibre-reinforced soils because fibres do not just have a significantly

lower specific gravity than that of the soil particles; they are also a minor

physical component of the composite material. It is better to measure the

material stiffness for compaction control, which can be done by means of


compaction equipment integrating continuous control compaction (CCC)

(Falorca et al. 2011).

• The quality control may be done by conducting the plate load tests, which allow

direct characterization of the soil compressibility with the applied pressure, as

seen in Fig. 5.12.

• The ratio of porosity n to the volumetric cement content pvc, all expressed as

a percentage of the total volume, can be useful in the field control of cement-

stabilized fibre-reinforced soil. Based on the unconfined compressive strength

tests on specimens submerged for 24 h and achieving an average degree

of saturation of 87%, the following relationships have been suggested

to estimate the unconfined compressive strength qu (Consoli et al. 2010):

For cement-stabilized soil,

qu kPað Þ ¼ 2:2� 107n

p0:28vc

� ��3:08

R2 ¼ 0:98� � ð5:8Þ

0 200 400 600 8000

1

2

3

4

5

Load-bearing pressure, q (kPa)Se

ttlem

ent, r

( mm

)

Fig. 5.12 Results of the plate load tests conducted on randomly distributed monofilament PP

fibre-reinforced silty sand embankment (50 m long, 10 m wide and 0.6 m high), using a semi-rigid

circular plate, 300 mm in diameter, under repeated loading and unloading (Adapted from Falorca

et al. 2011)


For cement-stabilized fibre-reinforced soil,

qu kPað Þ ¼ 1:0� 107n

p0:28vc

� ��2:73

R2 ¼ 0:95� � ð5:9Þ

Equations (5.8) and (5.9) are relevant for specific materials (nonplastic silty

sand, classified as SM, Portland cement of high early strength, monofilament PP

fibres with fibre content ranging from 0 to 0.5%, cement content ranging from 0 to

8%) and test conditions, as considered by Consoli et al. (2010) in their experimental

study. Similar relationships may be developed for other materials and site condi-

tions for the specific field application. Attempts can also be made to present the

generalized relationships. During the quality control, once a poor compaction is

identified, it can be readily taken into account in the design, using these equations

and adopting corrective measures accordingly, such as the reinforcement of the

treated layer or the reduction in the load transmitted.

5.5 Scope of Research

As mentioned earlier, the actual behaviour of fibre-reinforced soils is not yet well

known because the current understanding is largely based on small-scale laboratory

investigations and very limited large-scale or field studies. Hence, further studies,

especially involving field tests and performance evaluation of different applica-

tions, are essentially required to better understand the behaviour of fibre-reinforced

soils so that the fibre-reinforcements can be routinely utilized based on a more

rational analysis and design. In spite of some limitations, reinforcing the soils with

discrete flexible fibres can be a cost-effective means of improving their perfor-

mance in several applications. Additionally the use of fibres from the waste

materials can reduce the disposal problem in an economically and environmentally

beneficial way. Detailed investigations are expected in the future on several aspects

of fibre-reinforced soils, including the following:

• Cost-effective mixing technique

• Optimum size and shape of fibres for different applications

• Durability of fibres in different physical and environmental site conditions

• Drainage and pore water pressure developments within the fibre-reinforced soil

• Effective stress concept for fibre-reinforced soil

• Creep behaviour of fibre-reinforced soil

• Freezing-thawing behaviour of fibre-reinforced soil

• Cyclic loading behaviour of fibre-reinforced soil

• Fibre-clay interface behaviour

• Generalized analysis and design methods for different specific applications of

fibre-reinforced soil

• Cost-benefit analysis of different applications of fibre-reinforced soil


It is expected that applications of fibres in mining, agricultural and aquacultural

engineering will also be reported significantly in the future, although the applica-

tions discussed here are equally applicable for similar projects in these areas.

Note that some wastes, such as the municipal solid wastes, may be physically

similar to randomly distributed fibre-reinforced soils, and, therefore, the concepts of

fibre-reinforced soil engineering, as presented in this book, are also equally appli-

cable to such wastes to manage their disposal and utilization.

Chapter Summary

1. The technique of reinforcing soils with discrete fibres has several advantages,

and hence this has become one of the cost-effective and environmentally

friendly ground improvement techniques in the present-day construction

practice.

2. There are a large number of applications of fibre-reinforced soils in civil and

other related engineering areas. Major applications can be categorized as

geotechnical applications, transportation applications, and hydraulic and

geoenvironmental applications.

3. Much care is required to obtain a reasonably uniform distribution of fibres

within the soil mass, especially when the fibre content is large. Mixing of fibres

with soil can be carried out using an oscillatory- or helical-type mixer to avoid

fibre segregation, dragging, balling and floating problems, which are associated

with commonly used blade-type mixers.

4. Fibre-reinforced soil structures can be designed by composite or discrete

approach. The composite approach considers the fibre-reinforced soil a homo-

geneous material, while the discrete approach uses the contributions of soil and

fibres separately in the design.

5. Orientation of fibres must be considered properly in analysis and design of

fibre-reinforced soil structures. For field applications, the fibre content and the

aspect ratio should be selected based on experimental observations with spe-

cific soil and fibres under consideration as these two parameters significantly

govern the behaviour of fibre-reinforced soil, and moreover, they can be

controlled easily.

6. Addition of fibres to the soil backfill behind a retaining wall increases the

stability of the wall with reduced lateral earth pressure and displacement of

the wall.

7. Overall stability of a shallow foundation constructed over the weak foundation

soil can be significantly improved by placing a compacted cement-stabilized

fibre-reinforced soil layer of a suitable thickness (say 0.3B, where B being the

width of the footing) over the weak foundation soil.

8. Benefits of reinforcing the pavement layers with fibres are generally expressed

in terms of an extension of service life of the pavement and/or a reduction in the

thickness of pavement layer. Traffic benefit ratio (TBR) and layer reduction

ratio (LRR) are two commonly used parameters for design of pavement layers.

9. Fibres can be used effectively in reducing the seepage through the body of

water-retaining soil structures, increasing the soil-piping resistance and

5.5 Scope of Research 175

controlling the desiccation cracks in compacted clay layers used in liner and

cover applications.

10. Some application experience and guidelines are available for successful appli-

cations of fibre-reinforced soils. Further studies, especially involving field tests

and performance evaluation, are expected to develop the confidence level for

different applications.


(Select the most appropriate answer to the multiple-choice questions from Q 5.1 to

Q 5.5.)

5.1 Tamping and vibration techniques for preparing the fibre-reinforced soil spec-

imens in moist condition lead to

(a) Vertical orientation of fibres

(b) Near-vertical orientation of fibres

(c) Horizontal orientation of fibres

(d) Near-horizontal orientation of fibres

5.2 Fibre inclusion in the pavement base soil

(a) Increases the dry unit weight

(b) Decreases the unconfined compressive strength

(c) Increases the CBR value

(d) Both (a) and (c)

5.3 The most suitable roller for compacting fibre-reinforced soils is

(a) Smooth wheel roller

(b) Vibratory rubber-tyred roller

(c) Sheepsfoot roller

(d) Grid roller

5.4 For protecting the synthetic fibres from UV degradation, the entire surface area

of fibre-reinforced soil embankment should be covered with a top soil layer

having a thickness of about

(a) 50 mm

(b) 100 mm

(c) 150 mm

(d) 200 mm

5.5 The beneficial effects of fibre reinforcement in soil can be enhanced signifi-

cantly by stabilizing the fibre-reinforced soil with cement in a suitable quantity,

say using cement content of

(a) 0.5–1%

(b) 1–5%

(c) 5–10%

(d) 10–20%


5.6 What are the advantages exhibited by the fibre-reinforced soils?

5.7 In the laboratory, prepare a mixture of sand and fibres by any suitable means in

dry and wet conditions, and compare your observations about the fibre orien-

tation with those reported by the researchers as presented in this chapter.

5.8 List the potential application areas for fibre reinforcement.

5.9 Describe the techniques for preparing the laboratory test specimens of fibre-

reinforced soil.

5.10 What kind of fibre orientations is present in rolled-compacted fibre-

reinforced construction fills?

5.11 What considerations are required for the selection of fibres?

5.12 What are the different approaches for design of fibre-reinforced soil struc-

tures? Discuss their merits and demerits.

5.13 How can you determine the lateral earth pressure on a retaining wall from

fibre-reinforced cohesionless soil backfill?

5.14 For a fibre-reinforced sand backfill supported by a 10-m high retaining wall

with a vertical back face, consider the following:




Fibre-soil interface friction angle, ϕi¼ 20∘


Volumetric fibre content, pvf¼ 1.25%

Determine the total active earth pressure from the fibre-reinforced sand

backfill on the retaining wall, assuming the fibre-reinforced sand behaves as

an isotropic material.

5.15 For a fibre-reinforced foundation sand bed supported by a 0.75-m wide

surface strip footing, consider the following:




Fibre-soil interface friction angle, ϕi¼ 20∘


Volumetric fibre content, pvf¼ 1.25%

Determine load-bearing capacity of the surface strip footing resting over

the fibre-reinforced sand bed, assuming the fibre-reinforced sand behaves as

an isotropic material.

5.16 How can you control the desiccation cracks in clay liners and covers?

5.17 Define the following terms and explain their practical significance:

(a) Traffic benefit ratio

(b) Layer reduction ratio

(c) Crack intensity ratio

(d) Crack reduction factor

5.5 Scope of Research 177

5.18 What considerations are required to design fibre-reinforced pavement

layers?

5.19 How can fibres help in using sand in top courses of a pavement?

5.20 Describe a practical method for improving the foundation soil using fibre

inclusions.

5.21 What is the effect of fibre inclusions into the soil backfill on the lateral earth

pressure against a retaining wall?

5.22 Can the use of fibres reduce the seepage through water-retaining structures?

Explain with the help of a neat sketch.

5.23 What is soil piping? What is the effect of fibres on piping resistance of soil?

5.24 Discuss the effect of fibre content on the hydraulic conductivity of medium

plasticity soil when it is reinforced with fibres.

5.25 With the help of a neat sketch, discuss the effect of fibre content on crack

reduction factor when fibres are included in clay layers?

5.26 Visit a local construction site where the soil is being reinforced with fibres.

Based on your observation, write a technical note, and identify the key

aspects of the application technique.

5.27 Why should water be added prior to inclusion of fibres into soil for creating

the fibre-reinforced soil?

5.28 List some major cares and considerations required for field applications of

fibre-reinforced soils.

5.29 What is the most effective method of fibre inclusions in soil? What are the

difficulties in mixing fibre and soil in a rotating drum mixer as the cement

concrete is prepared?

5.30 What do you mean by optimum mixing moisture content? What is its

practical significance and how you can estimate it?

5.31 Describe the procedure for an embankment construction using the fibre-

reinforced soil.

5.32 How can you increase the durability of natural fibres for their use as soil

reinforcement?

5.33 What are the benefits of inclusion of fibres into dredged sediments while

dewatering them through geotextile tubes?

5.34 Discuss the quality control considerations for applications of fibre-reinforced

soils.


5.1 (d)

5.2 (c)

5.3 (b)

5.4 (a)

5.5 (c)

5.14 166.8 kN/m

5.15 856.4 kPa


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Index

AAnalytical model, 126, 131, 154

Application guidelines, 148, 165

CCalifornia bearing ratio (CBR), 16, 45, 86–92Compaction, 5, 8, 11, 19, 37, 39, 45, 46, 53, 55,

60, 65, 66, 77–80, 89, 102, 105, 147,

156, 160, 164, 166–168, 172, 174

Compressibility, 5, 6, 8, 10, 12, 18, 23, 80–86,

104, 111, 146, 157, 168, 173

FFibre content, 15, 33, 34, 39–42, 46, 49, 50, 53,

55–64, 66–72, 74, 75, 77–86, 88–92, 95,

97–105, 122–125, 128, 131, 132, 134,

136–139, 141, 142, 152, 153, 157–167,

170–172, 174, 175, 177, 178

Fibre-reinforced soils, 1, 15–20, 23, 25, 27–30,

33–42, 45–47, 54, 62, 65, 67, 71–73, 79,

81, 85–87, 92, 94, 95, 98, 101–106,

116–134, 136, 137, 140, 142, 145–149,

152–157, 159–176

Fibres, 1, 15–17, 23, 25, 27–30, 33–42,

45–106, 111–113, 116–129, 131–142,

145–149, 152–158, 160–176

Field applications, 15, 17, 19, 27, 34, 45, 103,

145–149, 161–166, 174, 175, 178

LLoad-bearing capacity, 87, 92–95, 97, 98, 103,

150, 153, 154, 169, 177

MMultioriented inclusions, 17, 23, 38–42, 79

NNumerical models, 39, 134, 140, 161

PPermeability, 5, 7, 10, 12, 18, 23, 80–86, 104,

111, 146, 157, 172

RReinforced soil phases, 1–4, 23, 32–36, 74

Reinforcement, 1, 3, 5–13, 15–19, 23, 26, 29,

30, 45, 47, 48, 53–55, 57, 58, 61–67, 69,

70, 72, 74, 75, 77, 81, 83, 89, 91, 93–95,

97–99, 111–121, 136–141, 145–147,

149, 154, 156, 160–162, 166, 169–172,

174, 176–178

Reinforcing mechanisms, 53, 111, 145

Research scope, 45, 174, 175

SShear strength, 5, 9–11, 18, 23, 46–65, 72,

75, 76, 92, 97, 102, 103, 111,

114–127, 131–135, 140, 142, 148,

169, 172

Soil, 1, 3, 5–19, 23, 25, 27–30, 33–42,

45, 111–142, 145–149, 152–158,

160–176

Soil mechanics, 1, 5–12, 32, 34, 35, 37, 57,

87, 111


S.K. Shukla, Fundamentals of Fibre-Reinforced Soil Engineering,Developments in Geotechnical Engineering, DOI 10.1007/978-981-10-3063-5

181

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